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Q. 49

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Short Answer

The lens shown in FIGURE CP is called an achromatic doublet, meaning that it has no chromatic aberration. The left side is flat, and all other surfaces have radii of curvature R.

a. For parallel light rays coming from the left, show that the effective focal length of this two-lens system is , where and are, respectively, the indices of refraction of the diverging and the converging lenses. Don’t forget to make the thin-lens approximation.

b. Because of dispersion, either lens alone would focus red rays and blue rays at different points. Define and as for the two lenses. What value of the ratio makes for the two-lens system? That is, the two-lens system does not exhibit chromatic aberration.

c. Indices of refraction for two types of glass are given in the table. To make an achromatic doublet, which glass should you use for the converging lens and which for the diverging lens? Explain

Crown glass 1.525 1.517

Flint glass 1.632 1.616

d. What value of R gives a focal length of ?

a. The statement is proved below.

b. The value of the ratio is .

c. The required statement is explained below.

d. The value of is .

See the step by step solution

Step by Step Solution

Part (a) Step 1 : Given Information

We have to find out effective focal length of the two lens.

Part (a) Step 2 : Calculation

Here, is focal length, is refractive index and is radius of curvature of lens

Part (b) Step 1 : Given Information

we have to find what value of the ratio .

Part (b) Step 2 : Simplify

Here, is focal length of blue and is refractive index.

Part (c) Step 1 : Given Information

We have to find the for each type of glass.

Part (c) Step 2 : Simplification 

.

Here, is the refractive index for respective names.

Part (d) Step 1 : Given Information

We have to find focal length in expression for R.

Part (d) Step 2 : Explanation

.

Here, is refractive index and is the focal length of lens.

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