Question

Two light bulbs are 1.20 m apart. From what distance can these light bulbs be marginally resolved by a small telescope with a 4.50 cm -diameter objective lens? Assume that the lens is diffraction limited and λ =600nm.

Answer 1

given

a small telescope with a 4.50 cm -diameter objective lens

then d = 0.045 m

x = 1.2 m apart

λ = 600 nm

λ = 600 X 10^-9 m

using equation

x = 1.22 λ D / d

here D value is unknown and have to find

so rewriting the above equation

D = x d / 1.22 λ

D = 1.2 X 0.045 / 1.22 X 600 X 10^-9

D = 73770.4919 m

or

D = 7.37704919 X 10⁴ m

or

D = 73.770 km