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### Find the value of the angle of emergence ....

Find the value of the angle of emergence from the prism. Refractive index of the glass is $\sqrt 3$.

(1) $60^{\circ}$
(2) $30^{\circ}$
(3) $45^{\circ}$
(4) $90^{\circ}$

Solution

The incident ray is refracted twice before it emerges finally. Since first refraction involves normal incidence, the refracted ray goes undeviated as shown in the figure. The second refraction involves bending for which the angle of emergence $\theta$ can be calculated as follows:

$\mu \times sin 30^{\circ} = 1\times sin \theta$

$\Rightarrow \sqrt 3 \times \frac {1}{2} = sin \theta$

$\therefore \theta = 60^{\circ}$

### Sum of the coefficients in the expansion of $(x+y)^n$ ....
If the sum of the coefficients in the expansion of $(x+y)^n$ is 4096, then the greatest coefficient in the expansion is _ _ _ _ . Solution $C_0 + C_1 + C_2 + C_3 + ......................... + C_n =4096$ $\therefore 2^n = 4096 =2^{12}$ $\Rightarrow n = 12$ Greatest coefficient = ${}^{12}{C_6} = 924$