**Dear Students** , ( pre – draft )

Given below are the** subjective type** questions asked in the section** Optics in IIT JEE Physics during the last 15 years** . Answers to be published shortly.

**1.** In given figure, S is a monochromatic point source emitting light of wavelength l = 500 nm. A thin lens of circular shape and focal length 0.10 m is cut into two identical halves L_{1} and L_{2} by a plane passing through a diameter. The two halves are placed symmetrically about the central axis SO will a gap of 0.5 mm. The distance along the axis from S to L_{1 }and L_{2} is 0.15 m while that from L_{1} and L_{2} to O is 1.30 m. The screen at O is normal to SO. ( IIT JEE 1993 )

- If the third intensity maximum occurs at the point A on the screen, find the distance OA.
- If the gap betweenL
_{1}and L_{2}is reduced from its original value of 0.5 mm, will the distance OA increase, decrease, or remain the same

**2.** An image Y is formed of point object X by a lens whose optic axis is AB as shown in figure. Draw a ray diagram to locate the lens and its focus. If the image Y of the object X is formed by a concave mirror (having the same optic axis as AB) instead of lens, draw another ray diagram to locate the mirror and its focus. Write down the steps of construction of the ray diagrams. ( IIT JEE 1994)

**3.** A ray of light traveling in air is incident at grazing angle (Incident angle = 90^{o}) on a long rectangular slab of a transparent medium of thickness t = 1.0 m. The point of incidence is the origin A(0,0). The medium has a variable index of refraction n(y) given by- ( IIT JEE 1995 )

n(y) = [ky3/2 + 1]1/2 where k = 1.0 (meter)-3/2 . The refractive index of air is1.0.

(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 the 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.

**4.** Angular width of central maximum in the Fraunhofer diffraction pattern of a slit is measured. The slit is illuminated by light of wavelength 6000 Å. When the slit is illuminated by light of another wavelength, the angular width decreases by 30%. Calculate the wavelength of this light. The same decrease in the angular width of central maximum is obtained when the original apparatus is immersed in a liquid. Find refractive index of the liquid. ( IIT JEE 1996 )

**5**. A right angle prism (45^{o}-90^{o}– 45^{o}) of refractive index n has a plane of refractive index n1 (n1 < n) cemented to its diagonal face. The assembly is in air. The ray is incident on AB. ( IIT JEE 1996 )

i. Calculate the angle of incidence at AB for which the ray strikes the diagonal faced at the critical angle.

ii. Assuming n = 1.352, calculate the angle of incident at AB for which the refracted ray passes through the diagonal face undeviated

**6.** A double slit apparatus is immersed in a liquid of refractive index 1.33. It has slit separation of 1 mm and distance between the plane of slits and screen is 1.33 m. The slits are illuminated by a parallel beam of light whose wavelength in air is 6300 Å. ( IIT JEE 1996 )

i. Calculate the fringe width

ii. One of the slits of the apparatus is covered by a thin glass sheet of refractive index 1.53. Find the smallest thickness of the sheet to bring the adjacent minimum as the axis.

**7**. A thin plano- convex lens of focal length ¦ is split into two halves. One of the halves is shifted along the optical axis. The separation between object and image planes is 1.8 m. The magnification of the image formed by one of the half lens is 2. Find the focal length of the lens and separation between the halves. Draw the ray diagram for image formation. ( IIT JEE 1996 )

**8.** In Young’s experiment, the source is red light of wavelength 7 x 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 5^{th} bright fringe. Find the thickness of the plate. When the source is now change to green light of wavelength 5 x 10^{-7} m, the central fringe shifts to a position initially occupied by the 6^{th} bright fringe due to red light. Find the refractive index of glass for green light. Also estimate the change in fringe width due to the change in wavelength. ( IIT JEE 1997 )

**9.** A thin equiconvex lens of glass of refractive index m = 3/2 and of focal length 0.3 m in air is sealed into an opening at one end of a tank filled with water m = 4/3. On the opposite side of the lens, a mirror is placed inside the tank on the tank wall perpendicular to the lens axis, as shown in figure. The separation between the lens and the mirror is 0.8 m. A small object is placed outside the tank in front of. Find the position (relative to the lens) of the image of the object formed by the system. ( IIT JEE 1997 )

**10**. In a Young’s experiment, the upper slit is covered by a thin glass pate of refractive index 1.4, while the lower slit is covered by another glass plate, having the same thickness as the first one but having refractive index 1.7. Interference pattern is observed using light of wavelength 5400 Å. It is found that the point P on the screen, where the central maximum(n = 0) fall before the glass plates were inserted, now has ¾ the original intensity. It is further observed that what used to be the fifth maximum earlier lies below the point P while the sixth minima lies above P. Calculate the thickness of glass plate. (Absorption of light by glass plate may be neglected). ( IIT JEE 1997 )

( to continue ……… )