Question

An object is placed at a distance of 20 cm from the optical centre of a convex lens of focal length 30 cm find the distance of the image from the lens what will be the height of the image if the object is 2 cm tall

Answer 1

Answer:

Explanation:

Use the lens formula

1/f=1/v-1/u

1/30=1/v-(1/-20)

1/30=1/v+1/20

1/30-1/20=1/v

2-3/60=1/v

-1/60=1/v                    ;;;v =  -60 cm

m=h of image/h of object  =  v/u

=H/2= -60/-20

=H = 3*2

=H = 6 cm

Answer 2

Answer:

The distance of the image from the convex lens is equal to 60cm and the height of the image is equal to 6cm.

Explanation:

We have given,

The distance of the object from the convex lens, u = - 20cm

The focal length of convex lens, $f= 30cm$

Consider that 'v' is the distance of the image from the lens.

We know the lens maker formula:

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

Substitute the value of 'u' and 'f' in above written equation:

$\frac{1}{30}=\frac{1}{v}-\frac{1}{-20}$

$\frac{1}{30}=\frac{1}{v}+\frac{1}{20}$

$\frac{1}{v}= \frac{1}{30}-\frac{1}{20}$

$\frac{1}{v} =\frac{2-3}{60}$

$\frac{1}{v} =\frac{-1}{60}$

Take the reciprocal on both sides;

$v=-60cm$

We know that, the magnification is the ratio of height of image to height of an object.

$\frac{H_{i}}{H_{o}} =\frac{\big v}{\big u}$

Given, the height of an object, $H_{o}= 2cm$

$H_{i}=(H_{o})*(\frac{v}{u})$

$H_{i}=(2)*\frac{60}{20}$

Height of the image = 6cm.