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Chapter 36: Q25P (page 1110)

Find the separation of two points on the Moon’s surface that can just be resolved by the 200in=5.1mtelescope at Mount Palomar, assuming that this separation is determined by diffraction effects. The distance from Earth to the Moon is 3.8×105km. Assume a wavelength of 550nm for the light.

Short Answer

Expert verified

The wavelength of 550nm for the light is 50.0m.

Step by step solution

01

Given data

Resolving separation d=5.1m

Wavelength between earth and the moon L=3.8×105km

Wavelength of light λ=550 nm

02

Definition of diffraction effect

When a wave hits a barrier or aperture, numerous events are referred to as diffraction. It is described as the interference or bending of waves through an aperture or around the corners of an obstruction into the geometric shadow of the obstruction or aperture.

The first minimum at an angle θ is produced by diffraction via a circular aperture or a lens of diameter d , which results in a central maximum and concentric maxima and minima:

θ=1.22λd

03

Determining the wavelength of 550 nm for the light

Let the separation of two points be 'D'

Since θR=1.22λdand θR=DL

D=1.22λdL=1.22×550×10-95.1×3.8×108 mD=50.0m

Hence, the wavelength of 550nm for the light is 50.0m.

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Most popular questions from this chapter

(a) What is the angular separation of two stars if their images are barely resolved by the Thaw refracting telescope at the Allegheny Observatory in Pittsburgh? The lens diameter is 76 cm and its focal length is 14 m. Assume λ=550nm. (b) Find the distance between these barely resolved stars if each of them is 10 light-years distant from Earth. (c) For the image of a single star in this telescope, find the diameter of the first dark ring in the diffraction pattern, as measured on a photographic plate placed at the focal plane of the telescope lens. Assume that the structure of the image is associated entirely with diffraction at the lens aperture and not with lens “errors.”

An x-ray beam of wavelength A undergoes first-order reflection (Bragg law diffraction) from a crystal when its angle of incidence to a crystal face is , and an x-ray beam of wavelength undergoes third-order reflection when its angle of incidence to that face is . Assuming that the two beams reflect from the same family of reflecting planes, find (a) the interplanar spacing and (b) the wavelength A.

The two headlights of an approaching automobile are 1.4m apart. At what (a) angular separation and (b) maximum distance will the eye resolve them? Assume that the pupil diameter is 5.0mm, and use a wavelength of 550nm for the light. Also assume that diffraction effects alone limit the resolution so that Rayleigh’s criterion can be applied.

At night many people see rings (called entoptic halos) surrounding bright outdoor lamps in otherwise dark surroundings. The rings are the first of the side maxima in diffraction patterns produced by structures that are thought to be within the cornea (or possible the lens) of the observer’s eye. (The central maxima of such patterns overlap the lamp.) (a) Would a particular ring become smaller or larger if the lamp were switched from blue to red light? (b) If a lamp emits white light, is blue or red on the outside edge of the ring?

What is the smallest Bragg angle for x rays of wavelength 30 pm to reflect from reflecting planes spaced 0.30 nm apart in a calcite crystal?
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