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Chapter 18: Problem 55

If two lenses of power \(+5\) diopters are mounted at some distance apart, the combination will always behave like a diverging lens if the distance between them is (A) Greater than \(40 \mathrm{~cm}\) (B) Equal than \(40 \mathrm{~cm}\) (C) Equal to \(10 \mathrm{~cm}\) (D) Less than \(10 \mathrm{~cm}\)

Short Answer

Expert verified
The combination of two lenses of power +5 diopters will behave like a diverging lens when the distance between the lenses is more than 40 cm (greater than 40 cm).

Step by step solution

01

Understanding the Power of Lenses

Firstly, understand the given problem. Here, two lenses with a power of +5 diopters are used. The positive sign indicates that these are converging lenses. The task is to find out under what conditions these lenses would behave like a diverging lens.
02

Formulating the Lens Formula

Recall the lens formula and lens maker's formula. The lens formula is given by \(1/f = 1/v - 1/u\), where f is the focal length, v is the image distance, and u is the object distance. The lens maker's formula is given by \(1/f = (n-1)(1/r1 - 1/r2)\), where n is refractive index and r1, r2 are radii of curvature of lens surfaces.
03

Combination of Lenses Equation

The lens formula for the combination of lenses is given by \(P = P1 + P2 - d*P1*P2\), where P is the total power of the combination of lenses, P1 and P2 are the powers of the individual lenses, and d is the distance between the lenses. This formula is based on the assumption that d is small compared to the individual focal lengths of the lenses.
04

Plugging in the Values

Substitute the given power of lenses (+5 diopters) into the above formula, and rearrange it to solve for d. This will yield the distance at which the lenses will behave like diverging lenses.
05

Final Analysis

Lastly, compare the obtained distance with the provided options (40 cm, 10 cm) to determine under what conditions the combination would act as diverging lenses.

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Most popular questions from this chapter

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