Question

At what magnification F of a telescope with a diameter of the objective D = 6.0 cm is the illuminance of the image of an object on the retina not less than without the telescope? The pupil diameter is assumed to be equal to d₀ = 3.0 mm. The losses of light in the telescope are negligible.

Answer 1

If L is the luminance of the object, A is its area, s = distance of the object then light falling on the objective is

The area of the image formed by the telescope (assuming that the image coincides with the object) is Γ²A and the area of the final image on the retina is

Where f = focal length of the eye lens. Thus the illuminance of the image on the retin (when the object is observed through the telescope) is

When the object is viewed directly, the illuminance is, similarly,