An object $5 c m$ of height is placed at the distance of $25 c m$ in front of convex lens of focal length $10 c m$ . Determine the size (h'), magnification (m) and position of image (v) with proper signs? Assume object distance to be negative and object height to be positive.

h^{'} = 3.3 c m

v = - 16.67 c m

m = 0.67

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h^{'} = - 3.3 c m

v = - 16.67 c m

m = 0.67

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h^{'} = - 3.3 c m

v = 16.67 c m

m = - 0.67

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h^{'} = 4.3 c m

v = 15 c m

m = 1

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Solution

The correct option is C $h^{'} = - 3.3 c m$
$v = 16.67 c m$
$m = - 0.67$
Given:
Object distance, $u = - 25 c m$
Object height, $h = 5 c m$
Focal length, $f = 10 c m$

Using lens formula:
$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
$\frac{1}{10} = \frac{1}{v} - \frac{1}{u}$
$v = \frac{50}{3} = 16.67 c m$

The positive value of $v$ shows that the image is formed on the other side of the lens and hence, is real.

Magnification of the lens is given by:
$m = \frac{v}{u}$
$m = \frac{50 / 3}{- 25} = - 0.67$
The negative sign show that the image is inverted.

Magnification is also given by:
$m = \frac{h^{'}}{h}$
$- 0.67 = \frac{h^{'}}{5}$
$h^{'} = - 3.3 c m$

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An object 5 cm of height is placed at the distance of 25 cm in front of convex lens of focal length 10 cm. Determine the size (h'), magnification (m) and position of image (v) with proper signs? Assume object distance to be negative and object height to be positive.

An object $5 c m$ of height is placed at the distance of $25 c m$ in front of convex lens of focal length $10 c m$ . Determine the size (h'), magnification (m) and position of image (v) with proper signs? Assume object distance to be negative and object height to be positive.