Important numerical of wave optics
1. In a Young’s double slits experiment fringes are obtained on a screen placed at certain distance away from the slits . If the screen is moved by 5 cm towards the slit , the fringe width changes by 30 μm . Given that the slits are 1mm apart . Calculate the wavelength of the light used . Ans- 600 nm.
2. Laser light of wavelength 640 nm incident on the pair of slits produces interference pattern in which bright fringe is separated by 7.2 mm . Calculate the wavelength of another source of light which produces interference fringes separated by 8.1 mm using same arrangement . Also find the minimum value of the order (n) of bright fringes of shorter wavelength which coincide with that of the longer wavelength . ans- 720nm , 9 .
4. Yellow light of wavelength λ= 6000 A illuminate a single slit of width 1 x 10-4 m calculate (i) the distance between two dark lines on either side of the central maximum when the diffraction pattern is on screen kept 1.5 m away from the slits , (ii) the angular spread of the first diffraction minima .
Ans- 1.8 cm , 6x 10-3 rad .
5. Two wavelength of sodium light 590 nm are used in turn , to study the diffraction taking place at the single slit of aperture 2x 10-4 m . The distance between the slits and the screen is 1.5 m . Calculate the separation between the position of first maxima of the diffraction pattern obtained in the two cases .
Ans-6.75×10-5m .
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6. (a) In a single slit diffraction , a slit of width d is illuminated by red light of wavelength 650 nm . For what value of d will (i) the first minimum fall at an angle of diffraction of 300 , and (ii) the first maximum fall at an angle of diffraction of 300 ?
(b) Why does the intensity of secondary maximum becomes less as compared to the central maximum .
Ans- 1.3 x10-6 m , 1.95×10 ‑6‑ m
7. (i) Draw a graph showing the variation of intensity ‘I’ of polarised light transmitted by an analyser with angle ‘ϴ’ between polariser and analyser . (ii) What is the value of refractive index of a medium of polarising angle 600 . Ans- ip =600 , √3 .
8. Two polaroids are set in crossed positions. A third polaroids is placed between the two making an angle ϴ with the pass axis of the first polaroid . Write the expression for the intensity of light transmitted from the second polaroid . In what orientations will the transmitted intensity be (i) minimum and (ii) maximum ?
Ans- 0 or ∏/2 ; 450
9. Two polaroids P1 and P2 are setup so that their pass axis are crossed with respect to each other . A third polaroid P3 is now introduced between these two so that its pass axis makes an angle ϴwith the pass axis of P1 . A beam of unpolarised light of intensity I0 is incident on P1 . If the intensity of light that gets transmitted through the combination of three polaroids , be I find the ratio of I/I0 when ϴ equals (i) 300 (ii)450 . Ans- 3I0/32 ; 3/4
10. . Two polaroids P1 and P2 are setup so that their pass axis are crossed with respect to each other . A third polaroid P3 is now introduced between these two so that its pass axis makes an angle 300 with the pass axis of P1 . A beam of unpolarised light of intensity I0 is incident on P1 . If the intensity of light that gets transmitted through P1 ,P2 and P3 . Ans- I1=I0/2 I2 =3I0/8 , I3= 3I0/32
11. A monochromatic light of wavelength 500 nm is incident normally on a single slit of width 0.2 mm to produce a diffraction pattern . Find the angular width of the central maximum obtained on the screen . Also estimate the number of fringes obtained in YDSE with fringe width 0.5 mm , which can be accommodate within the region of total angular spread of the central maximum due to single slit . Ans- ϴ=0 to 2.5×10-3 ; n=D/2 ;D+1
12. A beam of light consisting of two wavelength 800nm and 600 nm is used to obtain the interference pattern in YDSE on a screen placed 1.4 m away . If the two slits are separated by 0.28mm , calculate the least distance from the central bright maximum where the bright fringes of the two wavelengths coincide .
Ans- n=3 ; 1.2 cm .
13. In YDSE using monochromatic light of wavelength λ, the intensity of light at a point on the screen where path difference is λ is K units . Find out the intensity of light of light at a point where path- difference is λ/3 .
14. The ratio of the intensity at minima to the maxima in YDSE is 9:25 , find the ratio of the width of the two slits , also find the ratio of amplitude . Ans- 16:1 .
15. Two wavelength of sodium light of 590 nm and 596 nm are used in turn to study the diffraction taking place at a single slit of aperture 2×10-6 m . The distance between the slit and the screen is 1.5 m . Calculate separation between the position of first maxima and of the diffraction pattern obtained in the two cases .
Ans- 6.75 nm .