QUESTION #8 Total Internal Reflection

At the interface between two materials having refractive indices n_1$n_1$ and n_2$n_2$ , the critical angle for reflection of an em wave is theta_1C$\theta_{1C}$ . The n_2$n_2$ material is replaced by another material having refractive index n_3$n_3$ , such that the critical angle at the interface between n_1$n_1$ and n_3$n_3$ materials is theta_2C$\theta_{2C}$ . If n_3 > n_2 > n_1$n_3 > n_2 > n_1$ ; fracn_2n_3 = frac25$\frac{n_2}{n_3} = \frac{2}{5}$ and sin theta_2C - sin theta_1C = frac12$\sin \theta_{2C} - \sin \theta_{1C} = \frac{1}{2}$ , then theta_1C$\theta_{1C}$ is [cite: 1, 2]

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QUESTION #17 Lenses

Let mathbfu$\mathbf{u}$ and mathbfv$\mathbf{v}$ be the distances of the object and the image from a lens of focal length f$f$ . The correct graphical representation of mathbfu$\mathbf{u}$ and mathbfv$\mathbf{v}$ for a convex lens when |mathbfu| > f$|\mathbf{u}| > f$ , is [cite: 1, 2]

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QUESTION #23 Refraction

Two light beams fall on a transparent material block at point 1 and 2 with angle theta_1$\theta_{1}$ and theta_2$\theta_{2}$ , respectively, as shown in figure. After refraction, the beams intersect at point 3 which is exactly on the interface at other end of the block. Given: the distance between 1 and 2, d = 4sqrt3 mathrm~cm$d = 4\sqrt{3} \mathrm{~cm}$ and theta_1 = theta_2 = cos^-1left(fracn_22n_1right)$\theta_{1} = \theta_{2} = \cos^{-1}\left(\frac{n_{2}}{2n_{1}}\right)$ , where refractive index of the block n_2 >$n_{2} >$ refractive index of the outside medium n_1$n_{1}$ , then the thickness of the block is ______ cm. [cite: 1, 2] {{IMG1}}

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