Chapter 13, Problem 7STP

To determine

To Choose: The correct option.

Explanation of Solution

Introduction:

A curved mirror is a mirror with a curved surface which reflects. The surface can be convex or concave. Many curved mirrors have surfaces shaped like part of a sphere but often other shapes are used in optical devices.

Given,

  

Object length is $225\text{cm}$

Formula:

Lens formula

  $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

Here, $u$ is the object distance, $v$ is the image distance and $f$ is the focal length.

Magnification $m=\frac{v}{u}$

Substitute, $250\text{ cm}$ for $u$ and $62.5\text{ cm}$ for $v$ in the lens formula.

  $\begin{array}{c}\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\\ \frac{1}{62.5}-\frac{1}{250}=\frac{1}{f}\\ f=\frac{250\times 62.5}{250-62.5}\\ f=83.3\text{ cm}\end{array}$

Since the focal length is $\text{83}\text{.3 cm}$ .

Then,

  $\begin{array}{c}\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\\ \frac{1}{v}-\frac{1}{225}=\frac{1}{83.3}\\ v=\frac{225\times 83.3}{225+83.3}\\ v=60.79\text{cm}\end{array}$

Now, Substitute $60.7\text{9}\text{cm}$ for $v$ and $225\text{cm}$ for $u$ in magnification equation

  $\begin{array}{c}m=\frac{v}{u}\\ m=\frac{60.79}{225}\\ =0.27\end{array}$

Therefore magnification is nearly equal to $0.30$

Conclusion:

The correct answer is C.