Apainting in an art gallery has height h and is hung so that its lower edge is a distance d above the eye of an observer. how far from the wall should the observer stand to get the best view?

Solution:

With reference to Fig. 1

Let 'x' be the distance from the wall

Then for DAC:

⇒

Now for the BAC:

⇒

Now, differentiating w.r.t x:

For maximum angle, = 0

Now,

0 = [/tex]\frac{d}{dx}[tan^{-1} \frac{d + h}{x} -  tan^{-1} \frac{d}{x}][/tex]

0 =

After solving the above eqn, we get

x =

The observer should stand at a distance equal to x =

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