Optics-08-PROBLEMS

PROBLEMS 1. (a) A convex lens of focal length 15 cm. and a concave mirror of focal length 30 cm. are kept with their optic axes PQ and RS parallel but separated in vertical direction by 0.6 cm as shown. Q The distance between the lens and mirror is 30 cm. An upright R S object AB of height 1.2 cm is placed on the optic axis PQ of the lens at a distance of 20 cm. from the lens. If A B is the image after refraction from the lens and reflection from the mirror, find the distance of A B from the pole of the mirror and obtain its magnification. Also locate positions of A and B with respect to the optic axis RS. (b) A glass plate of refractive indeed 1.5 is coated with a thin layer of thickness t and refractive index 1.8. Light of wavelength  traveling in air is incident normally on the layer. It is partly reflected at the upper and the lower surfaces of the layer and the two reflected rays interfere. Write the condition for constructive interference. If   648nm , obtain the least value of t for which rays interfere constructively. 2. The Young’s double stile experiment is done in a medium of refrac- y tive index 4/3. A light of 600 nm wavelength is falling on the slits 1 having 0.45 mm separation. The lower slit S2 is covered by a thin S O glass sheet of thickness 10.4 mm and refractive index 1.5. The S2 interference pattern is observed on a screen placed 1.5 m from the slits as shown. (a) Find the location of central maximum (bright fringe with zero path difference) on the y-axis. (b) Find the light intensity at point O relative to the maximum fringe intensity. (c) Now, if 600 nm light is replaced by white light of range 400 to 700 nm, find wavelengths of the light that forms maxima exactly at point O. All wavelengths in this problem are for the given medium of refractive index 4/3. (Ignore dispersion). 3. The x-y plane is the boundary between two transparent media. Medium –1 with Z  0 has a refrac- tive index and medium –2 with Z  0 has a refractive index . A ray of light in medium –1 given by the vector → A  6 3i  8 3j10k is incident on the plane of separation. Find the unit vector in the direction of the refracted ray in medium –2. 4. A prism of refractive index n1 and another prism of refractive index n2 are stuck together without a gap as shown in the figure. The angles of the prism are as shown. n1 and n2 depend on  , the 10.8 104 A B wavelength of light, according to n1  1.20  2 and 10.8  44 n2 1.45 2 where  is in nm (a) Calculate the wavelength 0 for which rays incident at any angle on the interface BC pass through without bending at the interface. (b) For light of wavelength 0 , find the angle of incidence i on the face AC such that the deviation produced by the combination of prisms is minimum. 5. A coherent parallel beam of microwave of wave length   0.5 nm falls on a Young’s double apparatus. The separation be- tween the slits is 1.0 mm. The intensity of microwaves is mea- x sured on a screen placed parallel to the plane of the slits at a distance of 1.0 m from it as shown in figure. (a) If the incident beam falls normally on the double slit apparatus, find the coordinates of all the minima on the screen. (b) if the incident beam makes an angle of 30º with the x-axis (as in the dotted arrow shown in the figure), find the y-coordinates of the first minima on either side of the central maximum. 6. In young’s experiment, the source is of red light of wavelength 7 107 m. When a thin glass plate of refractive index 1.5 at this wavelength is put in the path of one of the interfering beams, the central bright fringe shifts by 103 m to the position previously occupied by the 5th bright fringe. Find the thickness of the plate. When the source is now changed to green light of wavelength 5 107 m , the central fringe shifts to a position initially occupied by the 5th bright fringe due to red light. Also estimate the change in fringe width due to the change in wavelength. 7. A ray of light tavelling in air is incident at grazing angle (incident angle = 90º) on a long rectangular slab of a transparent medium of thickness t = 1.0m. as shown in figure. The point of incidence is the origin A (0, 0). The medium has a variable index of refraction n(y) given by n(y)  [Ky3 / 2 1]1/ 2 where K  1.0 (metre)3/ 2 The refractive indeed of air is 1.0 (a) Obtain a relation between the slope of the trajectory of the ray at a point B(x, y) in the medium and the incident angle at that point. (b) Obtain an equation for the trajectory y(x) of the ray in the medium. (c) Determine the coordinates (x1, y1) of the point P, where the ray intersects the upper surface of the slab-air boundary. (d) Indicate the path of the ray subsequently.