The refractive index of a material is 1.2. If velocity of light in vacuum is 3 × 108 ms–1, find the velocity of light in the material?
| Given, velocity of light in vacuum | = | 3 × 108 ms–1 |
| And refractive index of a material (μ) | = | 1.2 |
| ∴ μ | = | (refractive index of a material) / (velocity of light in material) |
| 1.2 | = | (3 × 108 ms–1) / (velocity of light in material) |
| velocity of light in material | = | (3 × 108 ms–1)/1.2 |
| = | 2.5 × 108 ms–1. |
The angle of incidence in air for a ray of light is 45°. If ray travels through water of refractive index 4/3, find angle of refraction?
| a μ w | = | (sin i)/(sin r) |
| ∴ sin r | = | (sin i)/(a μ w) |
| = | (sin 45)/[4/3] | |
| = | (3 × 0.7071)/4 | |
| ∴ sin r | = | 0.5303 |
 r |
= | sin– 1(0.5303) |
| = | 32° (approx) |
A glass block 3.6 cm thick is placed over a stamp. Calculate the height through which image of stamp is raised. Refractive index of glass is 1.5 ?
| a μg | = | Real depth/Apparent depth |
| ∴ 1.5 | = | 3.6 cm/Apparent depth |
| ∴ Apparent depth | = | 3.6 cm/1.5 |
| = | 2.4 cm. | |
| ∴ Height through which image is raised | = | (3.6 – 2.4) |
| = | 1.2 cm. |
A postage stamp placed under a glass, appears raised by 15 mm. If refractive index of glass is 1.5, calculate the actual thickness of glass slab?
| Let real thickness of glass | = | x |
| ∴ Apparent thickness | = | (x – 15 mm) |
| ∴ We know μ | = | Real depth/Apparent depth |
| 1.5 | = | x/x – 15 mm |
| ∴1.5 x – 22.5 mm | = | x |
| ∴ x | = | 45 mm. |
The refractive index of glass, when a ray of light travels from air to glass is 1.5. Calculate the refractive index when light travels from glass to air?
| a μ g | = | 1/g μ a |
| 1.5 |
= | 1/g μ a |
| ∴ g μ a | = | 1/1.5 |
| = | 0.67 |
The ratio between sine of angle of incidence in water to sine of angle of incidence in air is 0.75. Calculate a μ w
| w μ a | = | 1/a μ w |
| 0.75 |
= | 1/a μ w |
| ∴ a μ w | = | 1/0.75 |
| = | 1.33 |
A beam of light passes from air into a substance X. If the angle of incidence be 72° and the angle of refraction be 40°, calculate the refractive index of substance X.(Given : sin 72° = 0.951 and sin 40° = 0.642) ?
| Given, Angle of incidence, i | = | 72° |
| = | sin 72° | |
| = | 0.951 | |
| And, Angle of refraction, r | = | 40° |
| = | sin 40° | |
| = | 0.642 | |
| ∴ Refractive index | = | Sine of angle of incidence/Sine of angle of refraction |
| or μ | = | sin i/sin r |
| = | sin 72°/sin 40° | |
| = | 0.951/0.642 | |
| = | 1.48. | |
| Thus, the refractive index of substance X is 1.48. |
The refractive index of water is 1.33 and for glass is 1.50 with respect to air. What is the refractive index of glass with respect to water ?
| w μ g | = | (a μ g)/(a μ w ) |
| = | 1.50/1.33 | |
| = | 1.12 |
Thus, the refractive index of glass with respect to water is 1.12.
The refractive index of water is 4/3 and of glass is 3/2. What is the refractive index of glass with respect to water ?
| Given, aμw | = | 4/3 |
| aμg | = | 3/2 |
| Let speed of light in air be c | ||
| Speed of light in water νw | = | c/aμw |
| Speed of light in glass νg | = | c/aμg |
∴ Refractive index of glass with respect to water
| wμg | = | Speed of light in water ν w / Speed of light in glass νg |
| = | c/aμw / c/aμg | |
| = | aμw / aμg | |
| = | (3/2) / (4/3) | |
| = | 9/8 |
The refractive index of glass is 3/2. What is the critical angle for glass–air surface? (sin 42° = 2/3)
| If i is the critical angle, then sin ic | = | 1/μ |
| = | 1/3/2 | |
| = | 2/3 | |
| or sin ic | = | 42° (since sin 42° = 2/3) |
| or ic | = | 42 |
Light enters from air into a glass plate having refractive index 1.50. What is the speed of light in glass ? (The speed of light in vacuum is 3 x 108 m/s).
| Given, speed of light in vacuum | = | 3 × 108 m/s |
| And, refractive index of glass plate | = | 1.50 |
| Refractive index of glass | = | Speed of light in air (or vacuum)/Speed of light in glass |
| So, 1.50 | = | 3 × 108/Speed of light in glass |
| Speed of light in glass | = | 3 × 108/1.50 |
| = | 2 × 108 m/s | |
| Thus, the speed of light in glass is 2 × 108 m/s. |