Ray Optics - Problems

1. 1. Find the position of an object when placed in front of a concave mirror of a focal length
20 cm produces a virtual image twice the size of the object. (Ans: u =−10cm)
2. An object is placed in front of a convex mirror of focal length 60cm. if image formed is
half it's size, find the position of the image. (Ans: v = 30 cm.)
3. An object is placed 15cm from a convex mirror of radius of curvature 90cm. Calculate
image position and magnification. (Ans: m = 0.75
and v = 11.25 cm.)
4. An object is placed infront of a concave mirror of radius of curvature 40 cm at a
distance of 10 cm. Find the position, nature and magnification of the image.
(Ans. 20 cm behind the mirror, virtual, +2.)

2. 4. Question:
A concave mirror is held in water. What would be the change in the focal length of the mirror?
Ans:
Mirrors, spherical or otherwise, operate on the principle that the angle of reflection
of a ray of light equals the angle at which it strikes the mirror's surface. That behavior
is not affected by the medium in which the light travels, so the mirror's focal length
would be no different in air or water.

3. 5. Velocity of light in glass is 2×108 ms−1 and that in air is 3×108 ms−1. By how much
would an ink dot appear to be raised, when covered by a glass plate 6.0 cm thick?
(Ans: Dot will be raise by 2cm)
6. A ray of light of frequency of 5×1014Hz is passed through a liquid. The wavelength of
light measured inside the liquid is found to be 450×10−9m. Calculate refractive index of
the liquid. Ans. 1.33
7. What curvature must be given to the bounding surface of a refracting
medium (μ=1.5) for the virtual image of an object in the adjacent medium (μ=1) at 10 cm
to be formed at a distance of 40 cm? Ans: R = 8 cm

6. 8. A biconvex lens of focal length f is cut into two identical plano convex lenses. Focal length of each part will be?​
9. The optical density of turpentine is higher than that of water while its mass density is lower. Figure shows a layer of
turpentine floating over water in a container. For which one of the four rays incident on turpentine in figure, the path shown
is correct?
10. A symmetric biconvex lens of radius of curvature R and made of glass of refractive
index 1.5, is placed on a layer of liquid placed on top of a plane mirror as shown in the
figure. An optical needle with its tip on the principal axis of the lens is moved along the
axis until its real, inverted image coincides with the needle itslelf. The distance of the
needle from the lens is measured to be x. On removing the liquid layer and repeating the
experiment, the distance is found to be y. Obtain the expression for the refractive index
of the liquid in terms of x and y.

7. 11. Calculate the radius of curvature of an equi-concave lens of refractive index 1.5, when it is kept in a medium
of refractive index 1.4, to have a power of – 5 D. (R = 2.86 cm)