Question

The Figure shows a spherical concave mirror with its pole at $(0,0)$ and principal axis along the $x$-axis. There is a point object located at $(-40\text{cm},1\text{cm})$. Find the position of the image.

• A. $(\frac{-40}{7}\text{cm},\frac{1}{7}\text{cm})$
• B. $(\frac{-20}{7}\text{cm},\frac{-2}{7}\text{cm})$
• C. $(\frac{-40}{7}\text{cm},\frac{-1}{7}\text{cm})$
• D. $(\frac{40}{7}\text{cm},\frac{-1}{7}\text{cm})$

Answer 1

The correct option is C $(\frac{-40}{7}\text{cm},\frac{-1}{7}\text{cm})$

Given:
$u=-40\text{cm};h_0=1\text{cm};f=-5\text{cm}$

From mirror formula,

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}\Rightarrow \frac{1}{v}-\frac{1}{40}=\frac{1}{-5}$

$\Rightarrow v=\frac{-40}{7}\text{cm}$

As we know, from the definition of magnification,

$\frac{h_i}{h_o}=\frac{-v}{u}\Rightarrow h_i=\frac{-v}{u}{h}_o$

Substituting the given data we get,

$h_i=\frac{1}{-40}\times \frac{40}{7}\times 1=-\frac{1}{7}\text{cm}$

Since, a point object forms a point image.

Position of image $=(\frac{-40}{7}\text{cm},\frac{-1}{7}\text{cm})$

Hence, option (c) is the correct answer.