Question

A 12 inch telescope has an angular resolution how many times smaller when compared to a 4 inch telescope?

Answer 1

θ₂ = 3 θ₁

Step-by-step explanation:

given,

telescope of lens diameter = 12 inch

another telescope of lens diameter = 4 inch

comparison of resolution power.

Using the formula of resolution

`\theta = (1.22 \lambda)/(D)`

for diameter = 12 inch

`\theta_1 = (1.22 \lambda)/(D_1)`.....(1)

for diameter = 4 inch

`\theta_2 = (1.22 \lambda)/(D_2)`.......(2)

dividing equation (2) from (1)

`(\theta_2)/(\theta_1) = (D_1)/(D_2)`

now,

`(\theta_2)/(\theta_1) = (12)/(4)`

`(\theta_2)/(\theta_1) =3`

θ₂ = 3 θ₁

hence, we can say that resolution of telescope of 12 inch is 3 time smaller than the resolution of 4 inch telescope.