A12 inch telescope has an angular resolution how many times smaller when compared to a 4 inch telescope?

 θ₂ = 3 θ₁

Explanation:

given,

telescope of lens diameter = 12 inch

another telescope of lens diameter = 4 inch

comparison of resolution power.

Using the formula of resolution

for diameter = 12 inch

 .....(1)

for diameter = 4 inch

 .......(2)

dividing equation (2) from (1)

now,

 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.