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Chapter 35: Problem 2881

A convex lens of focal length \(f\) produces a real image \(x\) times the size of an object, Then what is the distance of the object from the lens? (A) \((\mathrm{x}+1) \mathrm{f}\) (B) \((\mathrm{x}-1) \mathrm{f}\) (C) \([(\mathrm{x}+1) / \mathrm{x}] \mathrm{f}\) (D) \([(x-1) / x] f\)

Short Answer

Expert verified
The distance of the object from the lens is \( u = \frac{(x-1)f}{x} \).

Step by step solution

01

Write down the lens formula and the magnification formula.

First, write down the lens formula and magnification formula, which will be used together to determine the object's distance from the lens. Lens formula: \( \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \) Magnification formula: \( m = -\frac{v}{u} \)
02

Replace m with x in the magnification formula

Since m = x, we can write the magnification formula using x: \( x = -\frac{v}{u} \)
03

Solve for v in the magnification formula.

Now, solve for v in the magnification formula: \( v = -xu \)
04

Substitute v in the lens formula.

Replace v with the expression found in Step 3 in the lens formula: \( \frac{1}{f} = \frac{1}{-xu} - \frac{1}{u} \)
05

Simplify and solve for u.

Simplify the equation and solve for u: \( \frac{1}{f} = \frac{1-x}{xu} \) Multiplying both sides by f and xu, we get: \( xu = (-x+1)f \) Now, divide both sides by x: \( u = \frac{(-x+1)f}{x} \) Comparing our result with the given options, we find that it matches Option (D). Thus, the distance of the object from the lens is: \( u = \frac{(x-1)f}{x} \).

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Most popular questions from this chapter

A spherical mirror forms an erect image three times the linear size of the object. If the distance between the object and the image is \(80 \mathrm{~cm}\), What is the focal length of the mirror? (A) \(30 \mathrm{~cm}\) (B) \(40 \mathrm{~cm}\) (C) \(-15 \mathrm{~cm}\) (D) \(15 \mathrm{~cm}\)

A convex lens of focal length \(\mathrm{f}\) is placed somewhere in between an object and a screen. The distance between the object and the screen is \(\mathrm{x}\). If the numerical value of the magnification product by the lens is \(\mathrm{m}\), What is the focal length of the lens? (A) \(\left[\mathrm{mx} /(\mathrm{m}-1)^{2}\right]\) (B) \(\left[\mathrm{mx} /(\mathrm{m}+1)^{2}\right]\) (C) \(\left[(m-1)^{2} / \mathrm{m}\right] \mathrm{x}\) (D) \(\left[(\mathrm{m}+1)^{2} / \mathrm{m}\right] \mathrm{x}\)

A short linear object of length \(L\) lies on the axis of a spherical mirror of focal length of \(f\) at a distance \(u\) from the mirror. Its image has an axial length \(L^{\prime}\) equal to \(\ldots \ldots \ldots\).. (A) \(\mathrm{L}[\mathrm{f} /(\mathrm{u}-\mathrm{f})]^{2}\) (B) \(\mathrm{L}[(\mathrm{u}-\mathrm{f}) / \mathrm{f}]^{2}\) (C) \(\mathrm{L}[(\mathrm{u}+\mathrm{f}) / \mathrm{f}]^{1 / 2}\) (D) \(L[f /(u-f)]^{1 / 2}\)

A concave lens of focal length \(\mathrm{f}\) forms an image which is n times the size of the object. What is the distance of the object from the lens? (A) \((1+\mathrm{n}) \mathrm{f}\) (B) \((1-\mathrm{n}) \mathrm{f}\) (C) \([(1-\mathrm{n}) / \mathrm{n}] \mathrm{f}\) (D) \([(1+\mathrm{n}) / \mathrm{n}] \mathrm{f}\)

A concave mirror of focal length \(\mathrm{f}\) produces an images n times the size of the object. If the image is real then What is the distance of the object from the mirror? (A) \((\mathrm{n}+1) \mathrm{f}\) (B) \([(\mathrm{n}-1) / \mathrm{n}] \mathrm{f}\) (C) \((\mathrm{n}-1) \mathrm{f}\) (D) \([(\mathrm{n}+1) / \mathrm{n}] \mathrm{f}\)
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