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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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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Point-to-Point Image Formation
In the world of telescopes, especially those using concave mirrors, achieving a focused image is crucial. This process is called point-to-point image formation.
Think of it as all the light rays that reflect off a concave mirror arranging themselves in such a way that they meet at a single point鈥攖he focus.
This focusing action allows telescopes to capture clear, sharp images of distant celestial objects.
  • The importance lies in precision: aligning light rays correctly reduces blurring.
  • This focused point is where an image forms, helping astronomers observe space details.
To achieve this clarity, we need mirrors that can manage to focus all kinds of light rays uniformly, eliminating potential distortions.
Spherical Aberration
Spherical aberration is a common problem that occurs with spherical mirrors. A spherical mirror is essentially a section of a sphere.
These mirrors do not provide a perfect point-to-point image formation because of their shape. Light rays that hit near the edge of the mirror tend to focus at a point that is slightly different from rays hitting the center.
This mismatch results in a blurry or distorted image.
  • The deviation happens because of the curvature of the sphere.
  • It's more evident in larger mirrors because they gather more light from various angles.
Understanding spherical aberration helps astronomers and engineers design better telescopes. They know they need to address this flaw, ensuring that telescopic observations remain reliable and accurate.
Parabolic Mirror
A parabolic mirror is a special type of mirror preferred in telescopes to overcome issues like spherical aberration. The surface of a parabolic mirror is shaped like a paraboloid, derived from revolving a parabola around its axis.
Unlike spherical mirrors, parabolic mirrors can bring all incoming light rays, irrespective of their origin, to a single focal point.
This feature helps create sharp and clear images, ideal for detailed astronomical observations.
  • The equation of a parabola is often written as \( y = ax^2 \).
  • This shape naturally corrects path differences in light rays.
  • Parabolic mirrors are often used in high-performance telescopes for precise imaging.
By using a parabolic mirror, a telescope can efficiently and effectively eliminate distortions and achieve crisp visuals of the universe.

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Most popular questions from this chapter

The law of reflection establishes a definite relationship between the angle of incidence of a light ray striking the boundary between two media and its angle of reflection. Describe this relationship.

One sometimes hears the expression, "It was like shooting fish in a barrel!" This usually is taken to mean that the task, whatever it was, was easy to complete. But is it really easy to shoot fish in a barrel? Only if you know some optics! Suppose you're in a boat and spy a large fish a few meters away. If you want to shoot the fish, how should you aim? Above the image of the fish? Below it? Directly at the image? Explain your choice. (You may assume that the path of the projectile you fire will not be deviated from a straight line upon entering the water, unlike light.)

Why are the Doppler effect and diffraction not as commonly observed with light as they are with sound?

Rank (from smallest to largest) the angle of refraction for a light ray in air entering each of the following substances with an angle of incidence equal to \(30^{\circ}\) : (i) water; (ii) benzene; (iii) dense flint glass; (iv) diamond.

Two light waves that have wavelengths of 700 and \(400 \mathrm{~nm}\) enter a block of glass (from air) with the same angle of incidence. Which has the larger angle of refraction? Why? Would the answer be different if the light waves were going from glass into air?
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