NEET Ray Optics — Set 18

Question 1

A concave lens of focal length $ 25 \, \text{cm} $ forms an image $ 10 \, \text{cm} $ from the lens. What is the object distance?

Accepted Answer

Focal length: $ f = -25 \, \text{cm} $ (concave lens). Image distance: $ v = -10 \, \text{cm} $ (virtual image). Lens formula: $ \frac{1}{v} - \frac{1}{u} = \frac{1}{f} $. $ \frac{1}{-10} - \frac{1}{u} = \frac{1}{-25} \Rightarrow \frac{1}{u} = \frac{1}{-10} - \frac{1}{-25} = \frac{-5 + 2}{50} = \frac{-3}{50} $. $ u = -\frac{50}{3} \approx -16.67 \, \text{cm} $.

Question 2

A prism of angle $ 60^\circ $ has a minimum deviation of $ 36^\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 = 60^\circ $, $ D_m = 36^\circ $. $ n = \frac{\sin \left( \frac{60 + 36}{2} \right)}{\sin \left( \frac{60}{2} \right)} = \frac{\sin 48^\circ}{\sin 30^\circ} $. $ \sin 48^\circ \approx 0.743 $, $ \sin 30^\circ = 0.5 $. $ n = \frac{0.743}{0.5} \approx 1.486 $.

Question 3

An object is placed $ 15 \, \text{cm} $ from a convex mirror of focal length $ 30 \, \text{cm} $. What is the magnification?

Accepted Answer

Focal length: $ f = 30 \, \text{cm} $, $ u = -15 \, \text{cm} $. Mirror equation: $ \frac{1}{v} + \frac{1}{-15} = \frac{1}{30} \Rightarrow \frac{1}{v} = \frac{1}{30} + \frac{1}{15} = \frac{1 + 2}{30} = \frac{3}{30} = \frac{1}{10} $. $ v = 10 \, \text{cm} $. Magnification: $ m = -\frac{v}{u} = -\frac{10}{-15} = 0.67 $.

NEET Physics: Ray Optics — Practice Set 18

Q1. A concave lens of focal length \( 25 \, \text{cm} \) forms an image \( 10 \, \text{cm} \) from the lens. What is the object distance?

Q2. A prism of angle \( 60^\circ \) has a minimum deviation of \( 36^\circ \). What is the refractive index?

Q3. An object is placed \( 15 \, \text{cm} \) from a convex mirror of focal length \( 30 \, \text{cm} \). What is the magnification?

Q4. A convex mirror of focal length \( 20 \, \text{cm} \) has an object placed \( 40 \, \text{cm} \) from it. What is the image distance?

Q5. A light beam converges to a point \( 15 \, \text{cm} \) away. A convex lens of focal length \( 10 \, \text{cm} \) is placed \( 5 \, \text{cm} \) from the convergence point. Where does the beam converge now?

Q6. A convex lens (\( f = 50 \, \text{cm} \)) and a concave lens (\( f = 25 \, \text{cm} \)) are in contact. What is the effective focal length?

Q7. A prism with refracting angle \( 60^\circ \) has a minimum deviation of \( 40^\circ \). What is the refractive index of the prism material?

Q8. A convex mirror of focal length \( 24 \, \text{cm} \) forms an image \( 8 \, \text{cm} \) behind the mirror. What is the object distance?

Q9. A convex lens of focal length \( 12 \, \text{cm} \) forms an image at \( 24 \, \text{cm} \) from the lens. What is the object distance?

Q10. In a concave lens, what is the effect on the image if the object is moved closer to the lens from a distant position?