First slide

Diffraction

Question

The aperture of the largest telescope in the wold is $\approx 5$ meters. If the separation between the moon and the earth is $\approx 4 \times 10^{5}$ km and the wavelength of visible light is $\approx 5000 Å$ then the minimum separation between objects on the surface of moon which can be just resolved is

Easy

A

$\approx 1 m$
B

$\approx 10 m$
C

$\approx 50 m$
D

$\approx 200 m$

Solution

If $θ$ be the angle of the cone of light from the object and d, the diameter of the object, then
$θ = \frac{1 \cdot 22 λ}{d} or d = \frac{1 \cdot 22 λ}{θ} Here θ = \frac{diameter of telescope}{distance of moon} = \frac{5}{(4 \times 10^{8})} d = [\frac{1 \cdot 22 \times (5000 \times 10^{- 10})}{\{5 / (4 \times 10^{8})\}}] \approx 50 m$

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