Question

How many times dimmer will an image be in a 8-inch telescope compared to a 20-inch telescope?

Answer 1

The intensity is the energy falling per unit area. If it is the same, then we get more energy for more area.

so, if we take a ratio of incoming energies through the telescopes

E₂₀/E₀₈ = A₂₀/A₀₈ area of circle is Pi*R²

where,

E₂₀= energy from 20-inch telescope

A₂₀= area of 20-inch telescope

R₂₀=radius of 20-inch telescope

E₀₈ =energy from 8-inch telescope

A₀₈ = area of 20-inch telescope

R₀₈=radius of 20-inch telescope

so, E₂₀/E₀₈ = R₂₀² / R₀₈² = 20²/8² = 6.25

so, the image from the 8-inch telescope will be 6.25 times dimmer than that of the 20-inch telescope.