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Chapter 5: Q41E (page 1213)

The VLBA (Very Long Baseline Array) uses a number of individual radio telescopes to make one unit having an equivalent diameter of about 8000 km. When this radio telescope is focusing radio waves of wavelength 2.0 cm, what would have to be the diameter of the mirror of a visible-light telescope focusing the light of wavelength 550 nm so that the visible-light telescope has the same resolution as the radio telescope?

Short Answer

Expert verified

The diameter of the mirror of a visible-light telescope is 220m.

Step by step solution

01

Rayleigh’s criterion

According to the Rayleigh criterion for the diffraction limit to resolution, two images are only resolvable when the center of one's diffraction pattern is directly over the first minimum of the other's diffraction pattern.

02

Diameter of the mirror of a visible-light telescope

Using the Rayleigh鈥檚 criterion, in both cases the setups have the same resolving power;

On putting the values;

Hence, the diameter of the mirror of a visible-light telescope is 220m.

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Most popular questions from this chapter

The laws of optics also apply to electromagnetic waves invisible to the eye. A satellite TV dish is used to detect radio waves coming from orbiting satellites. Why is a curved reflecting surface (a 鈥渄ish鈥�) used? The dish is always concave, never convex; why? The actual radio receiver is placed on an arm and suspended in front of the dish. How far in front of the dish should it be placed?

A convex spherical mirror with a focal length of magnitude 24.0 cm is placed 20.0 cm to the left of a plane mirror. An object 0.250 cm tall is placed midway between the surface of the plane mirror and the vertex of the spherical mirror. The spherical mirror forms multiple images of the object. Where are the two images of the object formed by the spherical mirror that are closest to the spherical mirror, and how tall is each image?

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The Galilean Telescope. Figure P34.100 is a diagram of a Galilean telescope, or opera glass, with both the object and its final image at infinity. The image serves as a virtual object for the eyepiece. The final image is virtual and erect. (a) Prove that the angular magnification is M=-f1/f2. (b) A Galilean telescope is to be constructed with the same objective lens as in Exercise 34.61. What focal length should the eyepiece have if this telescope is to have the same magnitude of angular magnification as the one in Exercise 34.61? (c) Compare the lengths of the telescopes. Figure P34.100

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