Question 97: Ray Optics

Question

Two thin convex lenses of focal lengths 30 cm and 10 cm are placed coaxially, 10 cm apart. The power of this combination is:

Accepted Answer

To find the power of a combination of two thin convex lenses, we use the formula for the equivalent focal length $ f_{	ext{eq}} $ of the lens system when the lenses are placed coaxially with a certain distance $ d $ between them:
$ \frac{1}{f_{	ext{eq}}} = \frac{1}{f_1} + \frac{1}{f_2} - \frac{d}{f_1 f_2} $
Given:
$ f_1 = 30 \, 	ext{cm} $
$ f_2 = 10 \, 	ext{cm} $
$ d = 10 \, 	ext{cm} $ (distance between the two lenses)
First, convert the focal lengths from centimeters to meters:
$ f_1 = 0.3 \, 	ext{m} $
$ f_2 = 0.1 \, 	ext{m} $
Plug in the values into the equation:
$ \frac{1}{f_{	ext{eq}}} = \frac{1}{0.3} + \frac{1}{0.1} - \frac{0.1}{(0.3)(0.1)} $
Calculate each term:
$ \frac{1}{0.3} = \frac{10}{3} \approx 3.33 $
$ \frac{1}{0.1} = 10 $
$ \frac{0.1}{(0.3)(0.1)} = \frac{0.1}{0.03} = \frac{10}{3} \approx 3.33 $
Substitute these calculated values back into the formula:
$ \frac{1}{f_{	ext{eq}}} = 3.33 + 10 - 3.33 $
$ \frac{1}{f_{	ext{eq}}} = 10 $
Thus, the power of the lens combination is:
$ 	ext{Power} = \frac{1}{f_{	ext{eq}}} = 10 \, 	ext{D} $
Therefore, the power of the lens system is 10 diopters (D).

Answer

5 D

Answer

1 D

Answer

20 D

Answer

10 D

Ray Optics

Two thin convex lenses of focal lengths 30 cm and 10 cm are placed coaxially, 10 cm apart. The power of this combination is:

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