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

angular resolution = 0.07270° = 1.269 ×
`10^(-3)` rad

greatest distance from the camera = 118.20 m = 0.118 km

Step-by-step 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 =
`(1.22* \lambda )/(D)` .......................1

put here value λ is wavelength and d is diameter

we get

sin θ =
`(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 =
`(I)/(r)` .................2

I =
`(15*10^(-2))/(1.269*10^(-3))`

I = 118.20 m = 0.118 km