SATHEE: Optics 2 Question 2

Optics 2 Question 2

2. A ray of light $A O$ in vacuum is incident on a glass slab at angle $60^{\circ}$ and refracted at angle $30^{\circ}$ along $O B$ as shown in the figure. The optical path length of light ray from $A$ to $B$ is

(2019 Main, 11 April I)

(a) $\frac{2 \sqrt{3}}{a} + 2 b$

(b) $2 a + \frac{2 b}{3}$

(d) $2 a + \frac{2 b}{\sqrt{3}}$

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Answer:

Correct Answer: 2. (c)

Solution:

From the figure,

$\begin{aligned} \cos 60^{\circ} & = \frac{a}{A O} \\ \Rightarrow & A O & = \frac{a}{\cos 60^{\circ}} = 2 a \\ and & \cos 30^{\circ} & = \frac{b}{B O} \\ or & B O & = \frac{b}{\cos 30^{\circ}} = \frac{2}{\sqrt{3}} b \end{aligned}$

Optical path length of light ray

$= A O + μ (B O)$

Here, $μ$ can be determined using Snell’s law, i.e.

$μ = \frac{\sin 60^{\circ}}{\sin 30^{\circ}} = \frac{\sqrt{3} / 2}{1 / 2} = \sqrt{3}$

Substituting the values from Eqs. (i), (ii) and (iv) in Eq. (iii), we get

$∴$ Optical path $= 2 a + (\sqrt{3} \times \frac{2}{\sqrt{3}} b)$

$= 2 a + 2 b$

Optics 2 Question 2

2. A ray of light $A O$ in vacuum is incident on a glass slab at angle $60^{\circ}$ and refracted at angle $30^{\circ}$ along $O B$ as shown in the figure. The optical path length of light ray from $A$ to $B$ is

Answer:

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Optics 2 Question 2

2. A ray of light AO in vacuum is incident on a glass slab at angle 60∘ and refracted at angle 30∘ along OB as shown in the figure. The optical path length of light ray from A to B is

Answer:

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Sample Mock Test

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2. A ray of light $A O$ in vacuum is incident on a glass slab at angle $60^{\circ}$ and refracted at angle $30^{\circ}$ along $O B$ as shown in the figure. The optical path length of light ray from $A$ to $B$ is