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Que 1st and 2nd with explanation.

1. A ray incident at point B at an angle of incidence $\theta $ enters into a glass sphere and is reflected and refracted at the farther surface of the sphere, as shown. The angle between the reflected and refracted rays at this surface is 90$\xb0$ . If refractive index of material of sphere is $\sqrt{3},$ the value of $\theta $ is

$a)\mathrm{\pi}/3\mathrm{b})\mathrm{\pi}/4\mathrm{c})\mathrm{\pi}/6\mathrm{d})\mathrm{\pi}/12$

2. Light in incident from glass $\left(\mu =1.5\right)$ to water $\left(\mu =\frac{4}{3}\right)$. Find the range of deviation for which there are two angle of incidence.

$a){\mathrm{sin}}^{-1}(8/9)to\mathrm{\pi}/2\mathrm{b})0\mathrm{to}{\mathrm{sin}}^{-1}(8/9)\mathrm{c})0\mathrm{to}{\mathrm{cos}}^{-1}(8/9)\mathrm{d}){\mathrm{cos}}^{-1}\left(8/9\right)\mathrm{to}\mathrm{\pi}/2$

2. Answer of the question 2 is given below .Kindly ask different question in different posts .

Here, if the angle of incidence is increased beyond critical angle, total internal reflection occurs and deviation decreases. So, the range of deviation is 0 to cos^{–1}(8/9).

Regards

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