Question

A thin prism, refracting angle A⁰ = 1⁰ = $\frac { \pi } { 180 }$ radian is kept in front of a concave mirror. The object is kept at the origin of the co-ordinate system. If the image is formed at co-ordinates (10 cm, $- \frac { \pi } { 24 }$ cm).Assuming para-axial ray approximation, determine the refractive index of prism –

• A. 2.5
• B. 1.5
• C. 2.0
• D. 3.0

Answer 1

Answer: (B)

1.5

Answer 2

d = (m – 1) A = $( \mu - 1 ) \times \frac { \pi } { 180 }$

I₁ act as an object for concave mirror.

After reflection at concave mirror final image will form after one more refraction at prism.

I₂I₃ = 5 × (m – 1) $\frac { \pi } { 180 }$

Distance of I₂ from axis = $\frac { \pi } { 24 } - ( \mu - 1 ) \frac { \pi } { 36 }$

Magnification at the second event

$| \mathrm { m } | = \left[ \frac { \frac { \pi } { 24 } - ( \mu - 1 ) \frac { \pi } { 36 } } { ( \mu - 1 ) \frac { \pi } { 12 } } \right]$

| m | = + $\frac { \mathrm { v } } { \mathrm { u } }$ = $\frac { 20 } { 30 }$= $\frac { 2 } { 3 }$

$\frac { 2 } { 3 } \times ( \mu - 1 ) \frac { \pi } { 12 }$ = $\frac { \pi } { 24 } - ( \mu - 1 ) \frac { \pi } { 36 }$

$\frac { ( \mu - 1 ) } { 3 }$+ $\frac { 2 } { 3 } ( \mu - 1 )$ = $\frac { 1 } { 2 }$

m – 1 = 0.5

m = 1.5