Question

hii friends.......A ray of light travels in the way as shown in figure. after passing through water, the rays grazes along the water air interface. if refractive index of water is 4/3, then refractive index of the glass will be​

Answer 1

refer to the attachment......

refractive index of the glass is =2

Answer 2

Note: The correct question must be provided with following options-

A ray of light travels in the way as shown in figure. After passing through water, the rays grazes along the water air interface. if refractive index of water is $4/3$, then refractive index of the glass will be​-

a) $\sqrt{3}$

b) $\frac{\sqrt{3}}{2}$

c) $\sqrt{2}$

d) $2$

Explanation for correct option

d:

Step 1: Given data

refractive index of water, $\mu_{w} =\frac{4}{3}$

angle of incidence,  $i=30^{\circ}$

refractive index of glass,  $\mu_{g} =?$

Step 2: Calculating the refractive index of glass

We know that, according to Snell's law-

$\mu_{g} sin\ i=\mu_{w} sin\theta$

put the given values in the above equation, we get-

$\mu_{g}\times sin\ 30^{\circ} =\frac{4}{3}\times sin\theta$

$\mu_{g}\times \frac{1}{2} =\frac{4}{3}\times sin\theta$

$\mu_{g} =\frac{8}{3}\times sin\theta---(1)$

Let, $i=90^{\circ}$

$\mu_{a} sin90^{\circ} =\mu_{w} sin\theta$

$1\times 1=\frac{4}{3}\times sin\theta$

$sin\theta=\frac{3}{4}$

put this in eq $(1)$ ,

$\mu_{g} =\frac{8}{3}\times \frac{3}{4} =\frac{8}{4}=2$

Thus, the refractive index of the glass is $2$.

Explanation for incorrect options

a,b,c:

Since, on evaluation, the refractive index is not equal to either $\sqrt{3}$ , $\frac{\sqrt{3}}{2}$ or $\sqrt{2}$, thus, options a,b and c are incorrect.

Hence, option d) is correct.

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