Question

With the help of a ray diagram, state what is meant by refraction of light. State Snell’s law for refraction of light and also express it mathematically.
The refractive index of air with respect to glass is 2/3 and the refractive index of water with respect to air is 4/3. If the speed of light in glass is 2 × 108 m/s, find the speed of light in (a) air, (b) water.

Answer 1

Answer:

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Explanation:

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Answer 2

Refraction of light:

• When the light ray passes from one medium to another medium, the light ray bends from its general path.
• This is due to different optical density of the medium.
• This phenomenon is called refraction of light.
• The ray diagram for refraction of light is given in the image below.

Snell’s law:

Snell's law states that the ratio of angle of incidence to sine of the angle of refraction is constant.

Its mathematical expression is:

$\bold{\frac{\sin \mathrm{i}}{\sin \mathrm{r}}=\mathrm{constant} = \mu^a_{b}}$

The absolute refractive index is ratio of speed of light in vacuum to speed of light in medium.

(a) Speed of light in air

The refractive index of air is given by the formula:

$\bold{\mu_{\mathrm{a}}=\frac{c}{\mathrm{V}_{\mathrm{a}}}}$

The refractive index of glass is given by the formula:

$\bold{\mu_{\mathrm{g}}=\frac{c}{\mathrm{V}_{\mathrm{g}}}}$

On dividing both the refractive indexes, we get,

$\bold{\frac{\mu_{\mathrm{a}}}{\mu_{\mathrm{g}}}=\frac{V_{\mathrm{g}}}{V_{\mathrm{a}}}}$

From question, the refractive index of air with respect to glass is 2/3

$\bold{\frac{\mu_{a}}{\mu_{g}}=\frac{V_{g}}{V_{a}}=\frac{2}{3}}$

$\bold{V_{a}=\frac{3}{2} \times V_{g}}$

$\bold{V_a=\frac{3}{2} \times 2 \times 10^{8} \ \mathrm{m} / \mathrm{s}}$

Thus, the velocity of light in air is:

$\bold{\therefore V_a=3 \times 10^{8} \ \mathrm{m} / \mathrm{s}}$

(b) Speed of light in water

The refractive index of water is given by the formula:

$\bold{\mu_{\mathrm{w}}=\frac{c}{V_{\mathrm{w}}}}$

The refractive index of glass is given by the formula:

$\bold{\mu_{\mathrm{a}}=\frac{C}{V_{\mathrm{a}}}}$

On dividing both the refractive indexes, we get,

$\bold{\frac{\mu_{w}}{\mu_{a}}=\frac{V_{a}}{V_{w}}}$

From question, the refractive index of water with respect to air is 4/3

$\bold{\frac{\mu_{\mathrm{w}}}{\mu_{\mathrm{a}}}=\frac{\mathrm{V}_{\mathrm{a}}}{\mathrm{V}_{\mathrm{w}}}=\frac{4}{3}}$

$\bold{V_{w}=\frac{3}{4} \times 3 \times 10^{8}}$

$\bold{V_w=\frac{9}{4} \times 10^{8}}$

$\bold{\therefore V_w=2.25 \times 10^{8} \ \mathrm{m} / \mathrm{s}}$