Question

Early cameras were little more than a box with a pinhole on the side opposite the film. (a) What angular resolution would you expect from a pinhole with a 0.50-mm diameter? (b) What is the greatest distance from the camera at which two point objects 15 cm apart can be resolved? (Assume light with a wavelength of 520 nm.

Answer 1

Answer:

angular resolution = 0.07270° = 1.269 × $10^{-3}$ rad

greatest distance from the camera = 118.20 m = 0.118 km

Explanation:

given data

diameter = 0.50 mm = 0.5 × $10^{-3}$ m

distance apart = 15 cm =  15× $10^{-2}$ m

wavelength λ = 520 nm = 520 × $10^{-9}$ m

to find out

angular resolution and greatest distance from the camera

solution

first we expression here angular resolution that is

sin θ = $\frac{1.22* \lambda }{D}$   .......................1

put here value λ is wavelength and d is diameter

we get

sin θ = $\frac{1.22*520*10^{-9}}{0.5*10^{-3}}$

θ = 0.07270° = 1.269 × $10^{-3}$ rad

and

distance from camera is calculate here as

θ = $\frac{I}{r}$    .................2

I = $\frac{15*10^{-2}}{1.269*10^{-3}}$

I = 118.20 m = 0.118 km