A parallel-sided block of glass with a refrac | vedclass

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(B) For normal refraction through multiple media,the apparent depth is given by the sum of the real depths divided by their respective refractive indi

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$3$

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(B) For normal refraction through multiple media,the apparent depth is given by the sum of the real depths divided by their respective refractive indices: $	ext{Apparent depth} = \sum \frac{t_i}{\mu_i}$.Let the total depth of the water be $H$. At point $B$,there is only water of depth $H$. Thus,the apparent depth $l_B$ is:$l_B = \frac{H}{4/3} = \frac{3H}{4}$.At point $A$,there is a glass block of thickness $t = 36 \, mm$ and refractive index $\mu_g = 1.5 = 3/2$,and the remaining water depth is $(H - 36) \, mm$. Thus,the apparent depth $l_A$ is:$l_A = \frac{H - 36}{4/3} + \frac{36}{3/2} = \frac{3(H - 36)}{4} + \frac{36 	imes 2}{3} = \frac{3H}{4} - 27 + 24 = \frac{3H}{4} - 3$.The difference between the apparent depths is:$\Delta l = l_B - l_A = \frac{3H}{4} - (\frac{3H}{4} - 3) = 3 \, mm$.

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