1. In the Young’s double – hole experiment (see Fig 14.6), the
distance between the two holes is 0.5 mm, λ = 5 × 10-5 cm and D = 50 cm.
What will be the fringe width? Get solution
2. Figure 14.23 represents the layout of Lloyd’s mirror experiment. S is a point source emitting waves of frequency 6 × 1014 sec-1. A and B represent the two ends of a mirror placed horizontally and LOM represents the screen. The distances SP, PA, AB and BO are 1 mm, 5 cm, 5 cm and 190 cm respectively. (a) Determine the position of the region where the fringes will be visible and calculate the number of fringes. (b) Calculate the thickness of a mica sheet (n = 1.5) which should be introduced in the path of the direct ray so that the lowest fringe becomes the central fringe. The velocity of light is 3 × 1010 cm/sec.... Get solution
3. (a) In the Fresnel’s biprism arrangement, show that d = 2 (n –1) aαwhere a represents the distance from the source to the base of the prism (see Fig. 14.19), α is the angle of the biprism and n the refractive index of the material of the biprism.(b) In a typical biprism arrangement b/a = 20 and for sodium light (λ = 5893 Å) one obtains a fringe width of 0.1 cm; here b is the distance between the biprism and the screen. Assuming n = 1.5, calculate the angle α. Get solution
4. In the Young’s double hole experiment a thin mica sheet (n = 1.5) is introduced in the path of one of the beams. If the central fringe gets shifted by 0.2 cm, calculate, the thickness of the mica sheet. Assume d = 0.1 cm, and D = 50 cm. Get solution
5. In order to determine the distance between the slits in the Fresnel biprism experiment, one puts a convex lens in between the biprism and the eye piece. Show that if D > 4 f one will obtain two positions of the lens where the image of the slits will be formed at the eye piece; here f is the focal length of the convex lens and D is the distance between the slit and the eye piece. If d1 and d2 are the distances between the images (of the slits) as measured by the eye piece, then show that .... What would happen if D f ? Get solution
6. In the Young’s double hole experiment, interference fringes are formed using sodium light which predominantly comprises of two wavelengths (5890 Å and 5896 Å). Obtain the regions on the screen where the fringe pattern will disappear. You may assume d = 0.5 mm and D = 100 cm. Get solution
7. If one carries out the Young’s double hole interference experiment using microwaves of wavelength 3 cm, discuss the nature of the fringe pattern if d = 0.1cm, 1cm and 4 cm. You may assume D = 100 cm. Can you use Eq. (21) for the fringe width? Get solution
8. In the Fresnel’s two mirror arrangement (see Fig. 14.18) show that the points S, S1 and S2 lie on a circle and S1S2 = 2bθ where b = MS and θ is the angle between the mirrors. Get solution
9. In the double hole experiment using white light, consider two points on the screen, one corresponding to a path difference of 5000 Å and the other corresponding to a path difference of 40000 Å. Find the wavelengths (in the visible region) which correspond to constructive and destructive interference. What will be the colour of these points? Get solution
10. (a) Consider a plane which is normal to the line joining two point coherent sources S1 and S2 as shown in Fig. 14.12. If S1P – S2P = Δ, then show that ... ... where the last expression is valid for D >> d. (b) For λ = 0.5 μm, d = 0.4 mm and D = 20 cm; S1O – S2O = 800 λ. Calculate the value of S1P – S2P for the point P to be first dark ring and first bright ring. Get solution
11. In continuation of the above problem calculate the radii of the first two dark rings for (a) D = 20 cm and (b) D = 10 cm. Get solution
12. In continuation of Problem 14.10 assume that d = 0.5 mm, λ = 5 × 10 –5 cm and D = 100 cm. Thus the central (bright) spot will correspond to n = 1000. Calculate the radii of the first, second and third bright rings which will correspond to n = 999, 998 and n = 997 respectively. Get solution
13. Using the expressions for the amplitude reflection and transmission coefficients [see Eqs. (67)-(72) in Chapter 24], show that they satisfy Stokes’ relations. Get solution
14. Assume a plane wave incident normally on a plane containing two holes separated by a distance d. If we place a convex lens behind the slits, show that the fringe width, as observed on the focal plane of the lens, will be f λ / d where f is the focal length of the lens. Get solution
15. In Problem 14.14, show that if the plane (containing the holes) lies in the front focal plane of the lens, then the interference pattern will consist of exactly parallel straight lines. However, if the plane does not lie on the front focal plane, the fringe pattern will be hyperbolae. Get solution
16. In the Young’s double hole experiment calculate I / Imax where I represents the intensity at a point where the path difference is λ/5. Get solution
2. Figure 14.23 represents the layout of Lloyd’s mirror experiment. S is a point source emitting waves of frequency 6 × 1014 sec-1. A and B represent the two ends of a mirror placed horizontally and LOM represents the screen. The distances SP, PA, AB and BO are 1 mm, 5 cm, 5 cm and 190 cm respectively. (a) Determine the position of the region where the fringes will be visible and calculate the number of fringes. (b) Calculate the thickness of a mica sheet (n = 1.5) which should be introduced in the path of the direct ray so that the lowest fringe becomes the central fringe. The velocity of light is 3 × 1010 cm/sec.... Get solution
3. (a) In the Fresnel’s biprism arrangement, show that d = 2 (n –1) aαwhere a represents the distance from the source to the base of the prism (see Fig. 14.19), α is the angle of the biprism and n the refractive index of the material of the biprism.(b) In a typical biprism arrangement b/a = 20 and for sodium light (λ = 5893 Å) one obtains a fringe width of 0.1 cm; here b is the distance between the biprism and the screen. Assuming n = 1.5, calculate the angle α. Get solution
4. In the Young’s double hole experiment a thin mica sheet (n = 1.5) is introduced in the path of one of the beams. If the central fringe gets shifted by 0.2 cm, calculate, the thickness of the mica sheet. Assume d = 0.1 cm, and D = 50 cm. Get solution
5. In order to determine the distance between the slits in the Fresnel biprism experiment, one puts a convex lens in between the biprism and the eye piece. Show that if D > 4 f one will obtain two positions of the lens where the image of the slits will be formed at the eye piece; here f is the focal length of the convex lens and D is the distance between the slit and the eye piece. If d1 and d2 are the distances between the images (of the slits) as measured by the eye piece, then show that .... What would happen if D f ? Get solution
6. In the Young’s double hole experiment, interference fringes are formed using sodium light which predominantly comprises of two wavelengths (5890 Å and 5896 Å). Obtain the regions on the screen where the fringe pattern will disappear. You may assume d = 0.5 mm and D = 100 cm. Get solution
7. If one carries out the Young’s double hole interference experiment using microwaves of wavelength 3 cm, discuss the nature of the fringe pattern if d = 0.1cm, 1cm and 4 cm. You may assume D = 100 cm. Can you use Eq. (21) for the fringe width? Get solution
8. In the Fresnel’s two mirror arrangement (see Fig. 14.18) show that the points S, S1 and S2 lie on a circle and S1S2 = 2bθ where b = MS and θ is the angle between the mirrors. Get solution
9. In the double hole experiment using white light, consider two points on the screen, one corresponding to a path difference of 5000 Å and the other corresponding to a path difference of 40000 Å. Find the wavelengths (in the visible region) which correspond to constructive and destructive interference. What will be the colour of these points? Get solution
10. (a) Consider a plane which is normal to the line joining two point coherent sources S1 and S2 as shown in Fig. 14.12. If S1P – S2P = Δ, then show that ... ... where the last expression is valid for D >> d. (b) For λ = 0.5 μm, d = 0.4 mm and D = 20 cm; S1O – S2O = 800 λ. Calculate the value of S1P – S2P for the point P to be first dark ring and first bright ring. Get solution
11. In continuation of the above problem calculate the radii of the first two dark rings for (a) D = 20 cm and (b) D = 10 cm. Get solution
12. In continuation of Problem 14.10 assume that d = 0.5 mm, λ = 5 × 10 –5 cm and D = 100 cm. Thus the central (bright) spot will correspond to n = 1000. Calculate the radii of the first, second and third bright rings which will correspond to n = 999, 998 and n = 997 respectively. Get solution
13. Using the expressions for the amplitude reflection and transmission coefficients [see Eqs. (67)-(72) in Chapter 24], show that they satisfy Stokes’ relations. Get solution
14. Assume a plane wave incident normally on a plane containing two holes separated by a distance d. If we place a convex lens behind the slits, show that the fringe width, as observed on the focal plane of the lens, will be f λ / d where f is the focal length of the lens. Get solution
15. In Problem 14.14, show that if the plane (containing the holes) lies in the front focal plane of the lens, then the interference pattern will consist of exactly parallel straight lines. However, if the plane does not lie on the front focal plane, the fringe pattern will be hyperbolae. Get solution
16. In the Young’s double hole experiment calculate I / Imax where I represents the intensity at a point where the path difference is λ/5. Get solution
