In a telescope, the magnification is 5 and the distance between the objective and eyepiece is 24 cm. What are the focal lengths of the objective and eyepiece lenses?

20 cm and 4 cm

30 cm and 6 cm

25 cm and 5 cm

None of these

Given:

Magnification M = 5

Distance between lenses L = f₀ + fₑ = 24 cm

Magnification formula M = f₀ / fₑ

Let's solve for f₀ and fₑ:

1. f₀ / fₑ = 5 => f₀ = 5fₑ

2. f₀ + fₑ = 24

Substituting f₀ = 5fₑ into the second equation:

5fₑ + fₑ = 24

6fₑ = 24

fₑ = 4 cm

Now, f₀ = 5fₑ = 5 × 4 = 20 cm