Question

In a convex lens an image formed which is 3times greater than the object , if the focal length of the lens is 25 cm then find the position of the object?

Answer 1

Answer:

The position of the object is 16.66cm away in front of the lens

Explanation:

Let us consider

•The focal length be f

• The size of the object be o

• The size of the image be i

• The object distance be u

• The image distance be v

The formula to be used

★ magnification , m = i/o = v/u

★ 1/v - 1/u = 1/f

Given data

f = 25cm

and i = 3o

By the formula of magnification

m = i/o = v/u

$\frac{3o}{o} = \frac{v}{u} \\ \implies3 = \frac{v}{u} \\ \implies3u = v \\ \implies v = 3u$

From lens formula we have

$\frac{1}{v} - \frac{1}{u} = \frac{1}{f} \\ \implies \frac{1}{3u} - \frac{1}{u} = \frac{1}{25cm} \\ \implies \frac{1 - 3}{3u} = \frac{1}{25cm} \\ \implies \frac{ - 2}{3u} = \frac{1}{25} \\ \implies3u = - 50cm \\ \implies u \: = \frac{ - 50}{3} \\ \implies u = - 16.66cm$

The object distance is -16.66

So , the object is 16.66cm away from the lens

Now using the value of u in the mirror formula

$\frac{1}{ v} - \frac{1}{ - 16.66} = \frac{1}{25} \\ \implies \frac{1}{v} = \frac{1}{25} - \frac{1}{16.66} \\ \implies \frac{1}{v} = \frac{ - 417}{20825} \\ \implies v = \frac{ - 20825}{417} \\ \implies v \: = - 49.94$

The image distance is -49.94cm

The '-' sign signify that the image will form in front of the lens .