A compound microscope is an optical instrument used for observing high magnified image of tiny objects. Magnifying power of compound microscope is defined as the ratio of the angle subtended at the eye by the final image to the angle subtended by the object , when both the final image and object at the least distance of distinct vision from the eye . It can be given that:m=mexm0, where me is the magnifying power of eyepiece and m0 is the magnifying power of objective lens. Suppose a lens of focal length 2.0cm and another of 6.25 cm separated by distance 15 cm .
(i) The object distance of eye piece , so that final image is formed at the least distance of distinct vision will be (a) 3.45cm (b)5cm (c)1.29cm (d) 2.59cm.
(ii)How far from the objective should an object be placed in order to obtain the condition given in (i). (a)4.5cm (b)2.5cm (c) 1.5cm (d) 3.0cm .
(iii) What is the magnifying power of the microscope in case of list distinct of vision? (a)20 (b)30 (c)40 (d)10 .
(iv) The intermediate image formed by the objective of a compound microscope is (a) real, inverted and magnified (b) real erect and magnified (c) virtual , erect and magnified (d) virtual, inverted and magnified .
(v) The magnifying power of compound microscope is increases with .(a) f0 increases and fe decreased (b)fe increased and f0 decreased (c) both increased (d) both decreased .
An astronomical telescope is an optical instrument which is used for observing distinct images of heavenly bodies libe stars, planets etc. It consists of two lenses . In normal adjustment of telescope , the final image is formed at infinity . Magnifying power of astronomical telescope in normal adjustment is defined as the ratio of the angle subtended at the eye by the angle subtended at the eye by the final image to the angle subtended at the eye , by the object directly , when the final image and the object both lie at the infinite distance from the eye . It is given by m = f0/fe. To increase magnifying power of an astronomical telescope in normal adjustment , focal length of objective lens should be small.
(i)An astronomical telescope of magnifying power 7 consists of two thin lenses 40cm apart , in normal adjustment . The focal length of the lenses are (a) 5cm,35cm (b) 7cm , 35cm (c)17cm , 35cm (d)5cm, 30cm.
(ii) An astronomical telescope has a magnifying power of 10. In normal adjustment , distance between the objective and eye piece is 22cm . the focal length of the objective lens is ,(a)25cm (b)10cm(c)15cm (d)20cm.
(iii) In astronomical telescope compare to eye piece , objective lens has (a)negative focal length (b)zero focal length (c)small focal length (d)large focal length .
(iv)To see stars use (a)simple microscope (b)compound microscope (c)endoscope (d)astronomical telescope.
(v)For large magnifying power of astronomical telescope (a) f0<<fe (b)f0=fe (c)f0>>fe (d)none of these .
Total internal reflection is the phenomenon of reflection of light into denser medium at the interface of denser medium with rarer medium . For this phenomenon to occur necessary condition is that light must move from denser to rarer and angle of incidence in denser medium must be greater than critical angle for the pair of media in contact. Critical angle depends on nature of medium and wavelength of light . We can show that µ=1/sinC (where C is the critical angle).
(i) critical angle for glass air interface , where µ for glass is 3/2 , is (a)41.80 (b) 600 (c)300 (d)150 .
(ii)Critical angle for water air interface is 48.60 , then what is the refractive index of water/(a)1 (b)3/2 (c)4/3 (d)3/4
(iii) critical angle for air water interface for violet colour is 490 its value for red colour will be (a)490(b)500 (c)480 (d)can’t say.
(iv) Which of the following is not due to total internal reflection?(a) working of optical fibre (b)difference between real depth and apparent depth of a pound.(c)mirage on hot summer day (d) brilliance of diamond.
(v) critical angle of glass is θ1 and that of the water is θ2 critical angle for water and glass surface would be (µg > µw) (a) less than θ2 (b) between θ1 and θ2 (c)greater then θ2 (d)less than θ1 .
2. Power of a lens-
Power (P) of a lens is given as the reciprocal of focal length (P=1/f)where f should be in meter and P is in Diopter . for convex power is positive and concave power is –ve. When two or more lenses are kept in contact then power of the combined lens is given as P= P1 + P2+P3 …….
(I) A convex and a concave lens is separated by distance d are then put in contact then the focal length of the combination (a) becomes 0 (b) remain the same (iii) decreases (iv)increases.
(ii)The two lenses of power +1.5D and +1.0D are placed in contact then the effective power of the combination will be (a)2.5D (b)1.5 D (c) 0.5D (d)3.25D .
(iii) If the power of the lens is 5D then what is the focal length of the lens?(a)10cm (b) 20cm (c)15cm (d) 5cm
(iv)Two thin lens of focal length +10cm and -5cm are kept in contact , the power of the combination is ? (a)-10D (b)-20D (c)10D (d)15D .
(v)A convex lens of focal length 25cm is placed coaxially in contact with a concave lens of focal length 20cm the system will be ; (a) converging in nature (ii) diverging in nature (c) can be converging or diverging (d) None of the above.
3.
4. Refraction through a prism
A prism is a portion of a transparent medium bounded by two planes face inclined to each other at a suitable angle . A ray of light suffers two refraction on passing through a prism and hence deviates through a certain angle from its original path . The angle of deviation of a prism is ɗ = (µ-1 )A , through which a ray deviates on passing through a thin prism of small refracting angle A . If µ is the refractive index of the material of the prism then the prism formula is µ = sin(A+ɗm/2)/sin(A/2).
(i) For which colour , angle of deviation is minimum ?(a) Red (b)yellow (c) violet (d) blue.
(ii) When white light moves through vacuum (a) all colours have same speed (b)different colours have different speed (c) violet has more speed then red (d)red has more speed then violet.
(iii)The deviation through a prism is maximum when angle of incidence is (a)450 (b) 700 (c)900(d)600 .
(iv)What is the deviation produced by a prism of angle 60 ? (µ=1.644) (a)3.840 (b)4.595(c)7.259(d)1.252.
(v) A ray of light falling at an angle of 500 is refracted through a prism and suffers minimum deviation . If the angle of prism is 600, then the angle of minimum deviation is (a) 450 (b) 750 (c)500 (d)400 .
This assignment provides Very important short answer type questions of ray optics which is very important for the class 12th board examinations.
1.What are the necessary conditions for the phenomenon of total internal reflection to occur . Also write the relation between refractive index and critical angle for a given pair of optical media.
2. State the principle on which the working of an optical fiber is based. What are the necessary conditions of phenomenon to occur?
3. Define critical angle . Obtain a relation between refractive index and critical angle for a pair of media . Does critical angle depends on the colour of light ? Explain.
4. Draw ray diagrams to show how specially designed prism make use of total internal reflection to obtain the inverted image of the object by deviating rays (i) through 900 (ii) through 1800.
5. Find the relation between real depth and apparent depth with the refractive index , when light moves from denser medium to rarer medium.
6. A fish in the water tank sees the outside world as if fish at the vertex of cone such that the circular base of the cone coincide with the surface of water . Given the depth of water were fish is located being h and critical angle for water-air interface being ic , find out by drawing the ray diagram the relationship between the radius of the cone and height h.
7. Draw the ray diagram showing the path of a ray of light entering through a triangular glass prism . Deduce the expression for the refractive index of glass prism in terms of the angle of minimum deviation and angle of the prism.
8. A convex lens of focal length f1 is kept in contact with another lens of focal length f2 . Find an expression for the focal length of the combination.
9. Why does the sun appear reddish at sunset or sunrise? For which colour the refractive index of prism material is maximum and minimum?
10. Draw the ray diagram showing formation of image by a magnifying glass when the image is formed at infinity also find the angular magnification of image.
11. Define the magnifying power of compound microscope when the final image is formed at infinity. Why does objective and the eyepiece of a compound microscope has short focal lengths ? explain.
12. Draw a schematic diagram of reflecting telescope (Cassegrain). Write its two advantages .or, Modern telescope prefer using suitable mirrors over using suitable lens , give two reasons for this preferences.
13. Use a lens formula and show that (i) Object placed at the focal length of the convex lens for image at infinity.(ii) Object is placed between O(optical center) and F (focus) the image will be virtual.
14. Draw a plot showing the variation of power of a lens with the wavelength of the incident light.
15 A double convex lens made from a material of refractive index µ1 is immersed in liquid of refractive index µ2 where µ2>µ1 . What change if any, would occur in the nature of the lens?
In this topic we will discuss what is optical fibre , what is its working and its important application.
Optical fibres – It is a device based on Total internal reflection by which signal may be transmitted from one location to another. It is a thin fibre of plastic specially coated glass , in which light enters at one end leaves it at other end suffering a number of total internal reflection with little loss of energy . it works even it is bent or twisted.
The structure of The structure of optical fibre consists of a core surrounded by cladding . Core ( very high quality glass/silica/plastic) is denser medium of refractive index µ1 and cladding ( glass/plastic) is relatively rarer medium of refractive index µ2 such that µ1 > µ2 .When light incident at one end of the core gets reflected and will be incident on the interface between the core and cladding at an angle greater then the critical angle and light continues reflecting in the core. After several reflection light comes out to the other side i.e. at the destination.
Application of optical fibre –
( I ) It is used to transmit light without loss of intensity over a long distance of several kilometers .
(ii) It is used in the in the manufacture of medical instruments, called endoscope for visual examination of stomach and intestines etc. of patients.
(iii) It used for telecommunication, i.e., in transmitting audio and video signals to long distance.
(iv) It is used to measure the blood flow to the heart in the form of photometric sensor.
(v) It is used to measure refractive indices of the liquid.
Application of total internal reflection ( T.I.R) –
T.I.R in nature and its technological application-
Brilliance of diamond- The brilliance of diamond is due to the total internal reflection of light. Refractive index for diamond is very large which is near about 2.42 , so that critical angle for diamond air is 24.40. The diamond is cut suitably so that light entering the diamond from any face falls at an angle greater than 24.40. Therefore , it suffers multiple T.I R. at various faces , and remains within the diamond , falling to come out . Hence the diamond sparkles.
Mirage– Mirage is an optical illusion of water observed generally in desert in hot summer day. An inverted image of an object such as tree is observed along with the object as if the tree were on the bank of a pound of water.
Optical fibres – It is a device based on Total internal reflection by which signal may be transmitted from one location to another. It is a thin fibre of plastic specially coated glass , in which light enters at one end leaves it at other end suffering a number of total internal reflection with little loss of energy . it works even it is bent or twisted.
The structure of The structure of optical fibre consists of a core surrounded by cladding . Core ( very high quality glass/silica/plastic) is denser medium of refractive index µ1 and cladding ( glass/plastic) is relatively rarer medium of refractive index µ2 such that µ1 > µ2 .When light incident at one end of the core gets reflected and will be incident on the interface between the core and cladding at an angle greater then the critical angle and light continues reflecting in the core. After several reflection light comes out to the other side i.e. at the destination.
Application of optical fibre –
( I ) It is used to transmit light without loss of intensity over a long distance of several kilometers .
(ii) It is used in the in the manufacture of medical instruments, called endoscope for visual examination of stomach and intestines etc. of patients.
(iii) It used for telecommunication, i.e., in transmitting audio and video signals to long distance.
(iv) It is used to measure the blood flow to the heart in the form of photometric sensor.
(v) It is used to measure refractive indices of the liquid.
Totally reflected glass prism – Prism designed to bend light by 900, or 1800 the phenomenon of total internal reflection , such prisms are used to invert images without changing their sizes.
A water tank appears shallower i.e. less deep then what actually is. When we observe an object which is inside the water or any transparent liquid it appear higher then its actual position . This is because when light travels from denser to rarer it bended away from the normal . And we can understand the inverse of this process that when a fish observe an object which is placed above the water level then it appears higher then its actual height from the surface of water this is because when light travels from rarer to denser medium light banded towards the normal.
To watch the video of this topic click on the link given below-
The relation between real depth and apparent with the refractive index is given in point 2 and point 3 below.
In this topic we will discuss , what do you mean by the term Total internal reflection, critical angle . And we will practice some questions based on these topics.
before to know this topic students must know Real depth and apparent depth. To know this topic click here-
Total internal reflection and critical angle.
Before to know about the total internal reflection we must know critical angle
Critical angle – It is the value of angle of incidence for which angle of refraction becomes 900, when light enters from denser to rarer medium .
As we know ,
1µ2 = sin i /sin r
Since light is moving from denser medium to rarer medium
So, 1µ2 = sin r /sin I;
i.e. µ = sin 900 / sin c [ here r= 900 then I is written by C (critical angle).
So, sin C = 1/µ
Then critical angle C = sin -1(1/µ).
Total internal reflection- (TIR) When the light in the denser medium strikes an interface separating the denser medium and a rarer medium at an angle of incidence greater then critical angle total light is reflected without any refraction through the rarer medium . This phenomenon is called “total internal reflection”.
As shown in fig.
I2< C ( critical angle) in this case refraction of light occurs .
I1> C in this condition T.I.R. occurs.
Essential conditions for T.I.R is
(i) Light must move from denser to rarer and (ii) angle of incidence should be greater then critical angle.
Questions based on refraction of light ( apparent depth and real depth, total internal reflection and
Q1. A ray of light is incident on a glass plate as an angle of 600. What would be the refractive index of glass , if reflected and refracted rays are perpendicular to each other? (a)√3 . (b)3/2 (c) √3/2 (d) ½ . ans-a
Q2. A glass of thickness 12mm is placed on a table . The lower surface of the slab has a black spot .At what depth from the upper surface will the sport appear when viewed from above ? (µg=1.50) . (a) 2mm (b) 4mm (c) 6mm (d) 8mm. ans-d
Q3. Light enters at an angle of incidence in a transparent rod of refractive index of the material of the rod the light once entered into it will not leave it through its lateral surface whatsoever be the value of angle of incidence? (a) µ>√2 (b) µ = 1 (c) µ=1.1 (d) µ=1.3. ans-a
Q4. A transparent cube contains a small air bubble . Its apparent distance is 2cm when seen through one face and 5cm when seen through other face . If the refractive index of the of the material of the cube is 1.5 the real length of the edge of the cube must be (a) 7cm (b) 7.5 cm (c) 10.5 cm (d) 14/3 cm. ans-c
Q5. For the given incident ray as shown in figure , The condition of T.I.R of the ray will be satisfied , if the refractive index of the block will be ,
(a) (√3+1)/2 (b)(√2+1)/2 (c)√3/√2 (d)√7/√6. ans-c
Q6. A ray of light travels from optical denser medium to rarer medium. The critical angle for the two media is C . The maximum possible deviation of the ray will be (a)2C (b) π/2 – C (c) π-C (d) π-2C . ans-b
Q7. The apparent depth of water in the cylindrical water tank of diameter 2R cm is reducing at the rate of x cm/min. when water is being drained out at a constant rate . The amount of water drained in cc/minute is : (µ1 refractive index of air and µ2 refractive index of water) (a) xπR2µ1/µ2 (b) xπR2µ2/µ1 (c)2πRµ1/µ2 (d) xπR2. ans-b
Q8. Refractive index of glass with respect to medium is 4/3 .If the difference between the velocities of light in medium and glass is 6.25 x 107m/sec , then velocity of light in medium is (a)2.5 x 108m/s (b) 0.125 x108m/s (c) 1.5 x 107m/s (d) 3 x 107m/s . ans-a
In this note we will discuss about the very important points on the refraction of light , every students must keep it in the mind . It is use ful for objective point of view.
Keep in your mind-
Some important thing for refraction of light.
1. Refractive index µ=c/v where c is the velocity of light in air or vacuum and v is the velocity of light in given medium.
2. The speed of light in air slightly less than the speed of light in vacuum.
3. The medium having greater refractive index is called denser and the other is rarer.
4. While going from a denser medium to rarer medium , the refracted ray bends away from the normal and vice-versa.
5. Snell’s low states that µ = sin I /sin r { µ>1 if light moves from rarer to denser and µ<1 if light moves from denser to rarer.}.
6. As we know 1µ2= v1/v2 ,
Therefore , 1µ2 x 2µ1=[v1/v2 x v2/v1]=1
Or ,
1µ2=1/ 2µ1 .
Similarly, 1µ2 x 2µ3x 3µ4 x…………..=1.
7. Laws of refraction is valid for all types of surface separating for two media i.e. the separating may be plane or curved.
8. The angle of deviation on refraction is given as ‘ angle of deviation’ =|i-r|.
9. If incident ray is normal, refraction takes place without bending. In this case I = r = 00.
15. Optical path is the distance travelled by light in vacuum in the same time travel in which it has travelled a distance x in a medium of refractive index µ . i.e. optical path = ct =cx/v=µx.
16 According to Cauchy’s formula, refractive index µ= A+ B/(wavelength)2.
Having saw this result we can say that, as wavelength increases refractive index decreases and vice-versa.
To solve the objective questions of this chapter ray optics click here-
In this topic we will get some, Very important questions of ray optics. Students preparing for board examination must solve all the questions given below.
Very important questions of ray optics
1. Derive the mathematical relation between refractive indices μ1 and μ2 of two radii and radius of curvature R for refraction at a convex spherical surfaces. Consider the object to be a point source on the principle axis in rarer medium of refractive index μ1 and a real image formed in the denser medium .
Light from a point source in air falls on a convex spherical glass surface of refractive index 1.5 and radius of curvature 20 cm . The distance of light source from the glass surface is 100cm . At what position the image will be formed?
2. A point object is placed in front of a double convex lens with its spherical faces of radii of curvature R1 and R2 . Show the path of rays due to refraction at first and subsequently at the second surface to obtain the formation of the real image of the object. Hence obtain the lens maker’s formula for a thin lens.
(i) A double convex lens having both faces of the same radius of curvature has refractive index 1.5. Find out the radius of curvature of the lens required to get the focal length of 20 cm . (ii) How the focal length of the above lens changes when it is placed in liquid of refractive index (a) 1.3 (b) 1.5 and (c)2.5 .
To solve this questions students must watch this video
3. Draw the ray diagram to show the refraction of a ray of monochromatic light passing through a glass prism. Deduce the expression for the refractive index of glass in terms of angle of prism and angle of minimum deviation.
A ray of light incident on face AB of an equilateral glass prism ABC , shows minimum deviation of 300 calculate the speed of light through the prism. Also find the angle of incidence at face AB so that the emergent ray along the face AC .
4.What do you mean by the term total internal reflection also write the conditions to get the total internal reflection, define the term critical angle for a pair of media , how the critical angle is related to the refractive index of the medium. A point source is kept at the bottom of the pond 2m deep ( μ= 4/3 )draw the ray diagram and calculate the area of water surface through which light emerges out of the pond.
5. Draw a ray diagram showing the image formation of compound microscope, hence obtain the expression for magnifying power when (I) image is formed at infinity (II) image is formed at least distance of distinct vision. (a)Why must both the objective and eyepiece of a compound microscope have short wavelength? (b) while viewing through a compound microscope, why should our eyes be placed not on the eye piece but at short distance away from it for best viewing?
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6. Draw a labelled ray diagram of astronomical telescope, for(I) normal adjustment, (II) at least distance of distinct of vision. Also derive the expression for magnifying power .You are given the three lance L1 , L2 , L3 having power 3D , 6D and 10D respectively with aperture 8cm,1cm and 1cm respectively, which two lances will you use as an eyepiece and objective to construct (a) compound microscope and (b) Astronomical telescope. Give reasons.
7.Explain reflecting type telescope draw the ray diagram for (I) Newtonian and (II)Cassegrainian type telescope. Write advantages of reflecting type telescope over refracting type telescope.
8.Derive lens formula in a convex lens using suitable ray diagram 1/v -1/u = 1/f . (a) A convex les is used to obtain the image of an object on the screen 10 cm from the lens . if the magnification is 19, find the focal length of the lens. (b) An illuminated object and a screen are placed 90 cm apart. Determine the focal length and nature of the lens required to produce a clear image on the screen , twice the size of the object.
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