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Photograph of Shadow



Well, actually the question was a bit different. It was asked by an eager mind from class 9th. The question was, "It is said that black hole does not reflect light. But, I have seen the mention of picture of black hole in a magazine. How is this possible?"

The answer is hidden in the "picture" of the shadow that can be seen in the photograph. Actually, it is not the photograph of the shadow that is taken but the light is blocked from certain portion and that is called shadow. The photograph is taken for the remaining portion and the place where the light is blocked is shadow.

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A man starts walking from the point P (-3, 4) ....

A man starts walking from the point P (-3, 4), touches the x-axis at R, and then turns to reach at the point Q (0, 2). The man is walking at a constant speed. If the man reaches the point Q in the minimum time, then $50 [(PR)^2 + (RQ)^2 ]$ is equal to _ _ _ _ . Solution For time to be minimum at constant speed, the directions must be symmetric. In other words, the angles made by PR and RQ with the vertical must be the same just like in the law of reflection in optics. $tan \theta = \frac {MP}{MR} = \frac {NQ}{NR} $ $\Rightarrow \frac {3-r}{4} = \frac {r}{2}$ $\Rightarrow r=1 $ So, $R \equiv ( - 1,0)$ Now, $50(PR^2+RQ^2)=50[(4+16)+(1+4)]=1250$
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