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Chapter 9: Problem 20

What is the ideal shape of concave mirrors used in telescopes?

Short Answer

Expert verified
Answer: The ideal shape of a concave mirror for telescopes is a parabolic mirror. This shape eliminates spherical aberration and ensures that all incoming light rays focus at the same point, resulting in clear and sharp images.

Step by step solution

01

Identify the properties of an ideal telescope mirror

An ideal telescope mirror must be able to focus all incoming light rays to a single point without any spherical aberrations. This is known as a 'point-to-point image formation.'
02

Explain the effect of a spherical mirror

A spherical mirror, also known as a concave mirror, is a mirror with a curved reflective surface. However, a spherical mirror will not produce a perfect point-to-point image, as the rays near the edge of the mirror will focus at different points than the rays near the center. This distortion is called 'spherical aberration.'
03

Introduce the concept of a parabolic mirror

A parabolic mirror is a type of concave mirror that has a surface that takes the shape of a paraboloid: a surface of revolution obtained by revolving a parabola around its axis. The equation for a parabola opening upward is given by \(y=ax^2\).
04

Explain the advantages of a parabolic mirror

A parabolic mirror eliminates spherical aberration because the light rays that reach the mirror surface, whether they are near the edge or the center, will focus at the same point. This allows a parabolic mirror to produce sharp and clear images, making it the ideal choice for a telescope mirror.

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