/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 13 A concave lens of focal length \... [FREE SOLUTION] | 91影视

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Chapter 18: Problem 13

A concave lens of focal length \(F\) produces an image equal to \(1 / n\) of size of object, the distance of the image, from the lens is (A) \((n+1) F\) (B) \((n-1) F\) (C) \(\left(\frac{n+1}{n}\right) F\) (D) \(\left(\frac{n-1}{n}\right) F\)

Short Answer

Expert verified
The distance of the image from the lens is \((n+1) F\), which corresponds to option (A).

Step by step solution

01

Write down the lens formula

The lens formula is given by the equation: \(\frac{1}{v} - \frac{1}{u} = \frac{1}{f}\), where v is the distance of the image from the lens, u is the distance of the object from the lens, and f is the focal length of the lens.
02

Write down the magnification formula

The magnification formula is given by the equation: \(M = \frac{h_i}{h_o} = \frac{-v}{u}\), where M is the magnification, \(h_i\) is the height of the image, and \(h_o\) is the height of the object. Since the image is 1/n times the size of the object, we can write the magnification formula as: \(\frac{1}{n} = \frac{-v}{u}\).
03

Solve the magnification formula for v

We can solve the magnification formula for v by multiplying both sides of the equation by u: \(v = -nu\).
04

Substitute the expression for v in the lens formula

We can now substitute the expression for v from Step 3 into the lens formula from Step 1: \(\frac{1}{-nu} - \frac{1}{u} = \frac{1}{F}\).
05

Simplify the lens formula

To simplify the lens formula, combine the fractions on the left side: \(\frac{-(1 + n)}{nu} = \frac{1}{F}\).
06

Solve the simplified lens formula for v

To solve the simplified lens formula for v, first take the reciprocal of both sides: \(\frac{nu}{-(1 + n)} = F\). Substitute the expression for v from Step 3: \(-nu = F(1 + n)\).
07

Determine the distance of the image from the lens

Divide both sides by -(1 + n) to isolate v: \(v = \frac{F}{-\frac{n}{n + 1}}\). Simplify the right side by multiplying top and bottom of the fraction by (n + 1): \(v = (n + 1)F\). Therefore, the distance of the image from the lens is (n+1)F, which corresponds to option (A).

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