A light source S is over the centre of a circular fixed opaque plate of radius r=1m at a distance a=2m from it. The distance from the plate to the screen is b=1m. Rate of increase of diameter of shadow formed on screen if source move towards the screen with speed 1m/s at a given instant will be

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A light source S is over the centre of a circular fixed opaque plate of radius r=1m at a distance a=2m from it. The distance from the plate to the screen is b=1m. Rate of increase of diameter of shadow formed on screen if source move towards the screen with speed 1m/s at a given instant will be

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P. Sai Srinivas 5th Jun, 2021

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Uttara 15th Jul, 2021

If we let the diameter of shadow be 2R. The given values of r=1,a=2 and b=1.

The tan theta angle will be r/a=R*(a+b),So the value of R after substitution comes to r*(a+b)/a= (1*(2+1))/2 =1.5 .Hence the final result diameter will be 2* r= 2*1.5 = 3meters

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