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Chapter 18: Problem 43

The relation between lateral magnification \(m\), object distance \(u\), and focal length \(f\) of a spherical mirror is (A) \(m=\frac{f-u}{f}\) (B) \(m=\frac{f}{f+u}\) (C) \(m=\frac{f+u}{f}\) (D) \(m=\frac{f}{f-u}\)

Short Answer

Expert verified
The correct relation between lateral magnification \(m\), object distance \(u\), and focal length \(f\) of a spherical mirror is (B) \(m=\frac{f}{f+u}\)

Step by step solution

01

Understanding Lateral Magnification

Lateral magnification, denoted as \(m\), for a spherical mirror is given by the ratio of the image height (\(h_i\)) to the object height (\(h_o\)). Additionally, it is also the ratio of the object distance (\(u\)) to the image distance (\(v\)) i.e \(m= \frac{h_i}{h_o} = -\frac{v}{u}\) where this negative sign indicates the inverted nature of the image.
02

Applying the Mirror Equation

By using the mirror equation \(\frac{1}{f} = \frac{1}{v} + \frac{1}{u}\), and solving it for \(v\), the image distance, it gives \(v=\frac{fu}{f+u}\).
03

Substituting the Image Distance in Magnification Equation

Replacing the computed value of the image distance \(v\) from the previous step into the formula of the lateral magnification, we get: \(m=-\frac{v}{u}=- \frac{fu}{f+u}\div u=-\frac{f}{f+u}\)

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Most popular questions from this chapter

A point object is placed at \(30 \mathrm{~cm}\) from a convex glass lens \(\left(\mu_{g}=\frac{3}{2}\right)\) of focal length \(20 \mathrm{~cm}\). The final image of object will be formed at infinity if (A) Another concave lens of focal length \(60 \mathrm{~cm}\) is placed in contact with the previous lens. (B) Another convex lens of focal length \(60 \mathrm{~cm}\) is placed at a distance of \(30 \mathrm{~cm}\) from the first lens. (C) The whole system is immersed in a liquid of refractive index \(\frac{4}{3}\). (D) The whole system is immersed in a liquid of refractive index \(\frac{9}{8}\)

Interference fringes were produced in Young's double slit experiment using light of wavelength \(5000 \AA\). When a film of thickness \(2.5 \times 10^{-3} \mathrm{~cm}\) was placed in front of one of the slits, the fringe pattern shifted by a distance equal to 20 fringe-widths. The refractive index of the material of the film is (A) \(1.25\) (B) \(1.35\) (C) \(1.4\) (D) \(1.5\)

A concave lens of focal length \(10 \mathrm{~cm}\) and a convex lens of focal length \(20 \mathrm{~cm}\) are placed certain distance apart. If parallel rays incident on one lens become converging after passing through other lens, then the separation between the lenses must be greater than (A) Zero (B) \(5 \mathrm{~cm}\) (C) \(10 \mathrm{~cm}\) (D) \(9 \mathrm{~cm}\)

The plane face of plano-convex lens of focal length 20 \(\mathrm{cm}\) is silvered. This combination is equivalent to the type of mirror and its focal length is (A) convex, \(f=20 \mathrm{~cm}\) (B) concave, \(f=20 \mathrm{~cm}\) (C) convex, \(f=10 \mathrm{~cm}\) (D) concave, \(f=10 \mathrm{~cm}\)

A telescope of diameter \(2 \mathrm{~m}\) uses light of wavelength \(5000 \AA\) for viewing stars. The minimum angular separation between two stars whose image is just resolved by this telescope is (A) \(4 \times 10^{-4} \mathrm{rad}\) (B) \(0.25 \times 10^{-6} \mathrm{rad}\) (C) \(0.31 \times 10^{-6} \mathrm{rad}\) (D) \(5.0 \times 10^{-3} \mathrm{rad}\)
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