Question

11. An object is 24 cm fraro the cenic of a meallic sphere, magnification of the image? Piere, 6 can in radius. What is the (8) 0.34 (b) -0.14 c) 0.11 (d) -0.11 le) 0.09 u= 24 ses 52 24

Answer 1

First we need to identify the image distance.

We have object distance 'u' = - 24 cm (since its lying to the left of our reflecting system).

Focal length of the metallic sphere = R/2 = 6/2 = 3 cm.

Plugging in to spherical mirror the formula, we have,

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

or,

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

$\frac{1}{v} = \frac{1}{3} - \frac{1}{-24}$

Solving this, we get

$\frac{1}{v} = \frac{8}{24} + \frac{1}{24} = \frac{9}{24}$

or, v = 24/9 cm.

The magnification 'm' is defined as

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

Using the values obtained above, we get -

$m = \frac{\frac{24}{9}}{24}$

That is, m = 1/9 ; or m = 0.11.

From the given options, it is option (c), m= 0.11