Question

A curved mirror brings collimated light to focus at x = 20 cm. as shown in figure (1). Then it is filled with water n = $\frac { 4 } { 3 }$ (as shown in Fig. (2)) and illuminated through a pinhole in a white card. A sharp image will be formed on the card at what distance, X?

• A. 10 cm
• B. 20 cm
• C. 30 cm
• D. 40 cm

Answer 1

Answer: (C)

30 cm

Answer 2

From (1), we find that the focal length of the mirror is f_a = 20 cm (in air).

Suppose the focal length is f_b when the mirror is filled with water. When paraxial rays are refracted at a plane surface, the object distance y and the image distance y' are related by

y' = $\frac { \mathrm { n } ^ { \prime } \mathrm { y } } { \mathrm { n } }$ , where n and n' are the refractive indices of the two media. As now y = f_a, n' = 1, n = 1.33, we have f_b = y' = $\frac { \mathrm { f } _ { \mathrm { a } } } { \mathrm { n } }$ = $\frac { 20 } { \left( \frac { 4 } { 3 } \right) }$ = 15 cm. For a concave mirror, if the object distance is equal to the image distance then it is twice the focal length, i.e., X = 2f_b = 30 cm.

where n and n' are the refractive indices of the two media. As now y = f_a, n' = 1, n = 1.33, we have f_b = y' = $\frac { \mathrm { f } _ { \mathrm { a } } } { \mathrm { n } }$ = $\frac { 20 } { \left( \frac { 4 } { 3 } \right) }$ = 15 cm. For a concave mirror, if the object distance is equal to the image distance then it is twice the focal length, i.e.,

X = 2f_b = 30 cm.