Concept explainers
(a)
The focal length of a thin lens in water is given by
(a)
Explanation of Solution
Given:
A thin lens whose focal length in air is
Introduction:
The focal length of a lens changes with change in the medium it is present.
The equation for refraction at a single surface relates the object distance, image distance, refractive indices of the media and the radius of curvature of the single surface lens.
Write the expression for the equation for refraction at water-lens interface.
Here,
Write the expression for the equation for refraction at lens-water interface.
Here,
Add equation (1) and (2).
Write the expression for thin lens equation.
Here,
Substitute
Here,
The focal length of a lens depends on the refractive index of lens, the medium in which lens is present and the radii of curvature of lens. It is expressed in form of lens maker’s formula.
Write the expression for lens maker’s formula.
Here,
Rearrange above equation for the value of
Substitute
Rearrange above equation for the value of
Conclusion:
Thus, the focal length of a thin lens in water is given by
(b)
The focal length of a double concave lens in air and water.
(b)
Explanation of Solution
Given:
Double concave lens has an index of refraction of
Formula used:
Write the expression for lens maker’s formula.
Here,
Calculation:
Substitute
Rearrange above equationfor
Write the expression for the focal length of a thin lens in water.
Here,
Substitute
Conclusion:
Thus, the focal length of lens in air is
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Chapter 32 Solutions
Physics For Scientists And Engineers Student Solutions Manual, Vol. 1
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