NEET Ray Optics — Set 13

Question 1

An object is placed $ 10 \, \text{cm} $ from a convex mirror of radius of curvature $ 30 \, \text{cm} $. What is the image distance?

Accepted Answer

$ f = \frac{R}{2} = \frac{30}{2} = 15 \, \text{cm} $. $ u = -10 \, \text{cm} $. $ \frac{1}{v} + \frac{1}{-10} = \frac{1}{15} \Rightarrow \frac{1}{v} = \frac{1}{15} + \frac{1}{10} = \frac{2 + 3}{30} = \frac{5}{30} = \frac{1}{6} $. $ v = 6 \, \text{cm} $ (virtual image).

Question 2

A prism of angle $ 50^\circ $ has a minimum deviation of $ 30^\circ $. What is the refractive index?

Accepted Answer

Refractive index: $ n = \frac{\sin \left( \frac{A + D_m}{2} \right)}{\sin \left( \frac{A}{2} \right)} $. $ A = 50^\circ $, $ D_m = 30^\circ $. $ n = \frac{\sin \left( \frac{50 + 30}{2} \right)}{\sin \left( \frac{50}{2} \right)} = \frac{\sin 40^\circ}{\sin 25^\circ} $. $ \sin 40^\circ \approx 0.643 $, $ \sin 25^\circ \approx 0.423 $. $ n = \frac{0.643}{0.423} \approx 1.52 $.

Question 3

A convex mirror of focal length $ 16 \, \text{cm} $ forms an image $ 8 \, \text{cm} $ behind the mirror. What is the object distance?

Accepted Answer

Focal length: $ f = 16 \, \text{cm} $ (convex mirror). Image distance: $ v = 8 \, \text{cm} $ (virtual image). Mirror equation: $ \frac{1}{v} + \frac{1}{u} = \frac{1}{f} $. $ \frac{1}{8} + \frac{1}{u} = \frac{1}{16} \Rightarrow \frac{1}{u} = \frac{1}{16} - \frac{1}{8} = \frac{1 - 2}{16} = \frac{-1}{16} $. $ u = -16 \, \text{cm} $.

NEET Physics: Ray Optics — Practice Set 13

Q1. An object is placed \( 10 \, \text{cm} \) from a convex mirror of radius of curvature \( 30 \, \text{cm} \). What is the image distance?

Q2. A prism of angle \( 50^\circ \) has a minimum deviation of \( 30^\circ \). What is the refractive index?

Q3. A convex mirror of focal length \( 16 \, \text{cm} \) forms an image \( 8 \, \text{cm} \) behind the mirror. What is the object distance?

Q4. A glass slab (\( n = 1.6 \)) of thickness \( 8 \, \text{cm} \) is placed over a point. What is the apparent shift?

Q5. Why does the image in a reflecting telescope remain free of chromatic aberration?

Q6. In a convex lens, what happens to the image if the object is placed between the focal point and twice the focal length?

Q7. A convex lens of focal length \( 18 \, \text{cm} \) has an object placed \( 36 \, \text{cm} \) from it. What is the image distance?

Q8. A ray of light passes from glass (\( n = 1.5 \)) to water (\( n = 1.33 \)) at an angle of incidence of \( 30^\circ \). What is the angle of refraction?

Q9. A prism of angle \( 50^\circ \) and refractive index \( 1.5 \) produces what minimum deviation?

Q10. A ray of light passes from air (\( n = 1 \)) to water (\( n = 1.33 \)) at an angle of incidence of \( 60^\circ \). What is the angle of refraction?