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Chapter 35: Q. 22 (page 1017)

A hydrogen discharge lamp emits light with two prominent wavelengths: 656nm(red) and 486nm(blue). The light enters

a flint-glass prism perpendicular to one face and then refracts

through the hypotenuse back into the air. The angle between

these two faces is 35掳.

a. Use Figure 35.18to estimate to 卤0.002the index of refraction

of flint glass at these two wavelengths.

b. What is the angle (in degrees) between the red and blue light

as it leaves the prism?

Short Answer

Expert verified

(a) The index of refraction of flint glass at these two wavelengths arenR=1.572andnB=1.587

(b) The angle between the red and blue light as it leaves the prism 1.16掳.

Step by step solution

01

part (a) step 1: Given Information

We need to estimate the index of refraction of flint glass at the two wavelengths.

02

part (a) step 2: Simply

位=656nmnR=1.572位=486nmnB=1.587.
Here位is the wavelength andnis refractive index.

03

part (b) step 1: Given Information

We need to find angle between the red and blue light.

04

part (b) step 2: Calculation

n1sin蟽1=n2sin蟽2蟽2=sin-1n1sin蟽1n2

RED: BLUE:

n1=1.572n1=1.587n2=1.00n2=1.00蟽1=35掳蟽1=35掳蟽2=64.37掳蟽2=65.54掳

蟽=蟽B-蟽R=1.16掳.

Here nis the refractive index and蟽refraction angle.

05

part (b) step 3: Diagram

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Most popular questions from this chapter

A microscope has a 20cmtube length. What focal-length objective will give total magnification localid="1649845070556" 500脳when used with an eyepiece having a focal length 5.0cm?

A reflection telescope is build with a 20cmdiameter mirror having a 1.00mfocal length. it is used with a 10Xeyepiece. what are

(a) the magnification and

(b) the f-numberof the telescope?

The resolution of a digital cameras is limited by two factors diffraction by the lens, a limit of any optical system, and the fact that the sensor is divided into discrete pixels. consirer a typical point-and--shoot camera that has a 20-mm-focal-lengthlens and a sensor with 2.5-渭m-widepixels.

(a) . First, assume an ideal, diffractionless lens, at a distance of 100m,what is the smallest distance, in cmbetween two point sources of light that the camera can barely resolve? in answering this question, consider what has to happen on the sensor to show two image points rather than one you can use S1=fbecauses>>f.

(b) . You can achieve the pixel-limied resolution of part a only if the diffraction which of each image point no greater than the diffraction width of image point is no greater than 1pixel in diameter. for what lens diameter is the minimum spot size equal to the width of a pixel ? use 600nmfor the wavelength of light.

(c). what is the f-numberof the lens for the diameter you found in part b? your answer is a quite realistic value of the f-numberat which a camera transitions from being pixel limited to being diffraction limited for f-numbersmaller than this (larger-diameter apertures), the resolution is limited by the pixel size and does not change as you change the apertures. for f-numberlarger than this (smaller-diameter apertures). the resolution is limited by diffraction and it gets worse as you "stop down" to smaller apertures.

An astronomer is trying to observe two distant stars. The stars are marginally resolved when she looks at them through a filter that passes green light with a wavelength near 550 nm. Which of the following actions would improve the resolution? Assume that the resolution is not limited by the atmosphere.

A. Changing the filter to a different wavelength. If so, should she use a shorter or a longer wavelength?

B. Using a telescope with an objective lens of the same diameter but a different focal length. If so, should she select a shorter or a longer focal length?

C. Using a telescope with an objective lens of the same focal length but a different diameter. If so, should she select a larger or a smaller diameter?

D. Using an eyepiece with a different magnification. If so, should she select an eyepiece with more or less magnification?

Once dark adapted, the pupil of your eye is approximately 7 mm in diameter. The headlights of an oncoming car are 120 cm apart. If the lens of your eye is diffraction limited, at what distance are the two headlights marginally resolved? Assume a wavelength of 600 nm and that the index of refraction inside the eye is 1.33. (Your eye is not really good enough to resolve headlights at this distance, due both to aberrations in the lens and to the size of the receptors in your retina, but it comes reasonably close.)
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