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Physics / Physics with MasteringPhysics 4 / Chapter 26 / Problem 93P

Physics with MasteringPhysics | 4th Edition | ISBN: 9780321541635 | Authors: James S. Walker

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The focal length of a lens is inversely proportional to

Chapter 26, Problem 93P

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QUESTION:

Problem 93P

The focal length of a lens is inversely proportional to the quantity (n − 1), where n is the index of refraction of the lens material. The value of n, however, depends on the wavelength of the light that passes through the lens. For example, one type of flint glass has an index of refraction of nr = 1.572 for red light and nv = 1.605 in violet light. Now, suppose a white object is placed 24.00 an in front of a lens made from this type of glass. If the red light reflected from this object produces a sharp image 55.00 cm from the lens, where will the violet image be found?

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QUESTION:

Problem 93P

The focal length of a lens is inversely proportional to the quantity (n − 1), where n is the index of refraction of the lens material. The value of n, however, depends on the wavelength of the light that passes through the lens. For example, one type of flint glass has an index of refraction of nr = 1.572 for red light and nv = 1.605 in violet light. Now, suppose a white object is placed 24.00 an in front of a lens made from this type of glass. If the red light reflected from this object produces a sharp image 55.00 cm from the lens, where will the violet image be found?

ANSWER:

Solution 93P

Step 1 of 4

Here we need to find the distance at which the violet light image is formed. In order to calculate the violet image distance, first we need to calculate the focal length for the red light and then the focal length of the violet light.

Given data,

Refractive index of red light, ${n}_{r}=1.572$

Refractive index of violet light, ${n}_{v}=1.605$

Object distance, ${d}_{o}=24\ cm$

Red light image distance, ${d}_{i,r}=55cm$

To find,

Violet light image distance, ${d}_{i,v}=?$

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