Question

18. An object 4 cm high is placed at a distance of 27 cm in front of a convex lens of focal length 18 cm
find the position, nature and size of the image formed.

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Answer 1

Explanation:

Given,

Object height,h=4 cm

Object distance,u=27 cm

Focal length,f=18 cm

Now,as we know

1/v-1/u =1/f

Therefore,1/v=1/f+1/u

=>1/v=1/18+1/27

=1/v=3/54+2/54

=1/v=5/54

=v=54/5

=v=10.8cm

Hence,the position of image is 10.8cm.

Positive sign of v shows that image must be real.

Now,

m=v/u=h'/h

=10.8/27=h'/4

=h'=43.2/27

=h'=1.6cm

Hence,the size of the image formed is 1.6 cm

Answer 2

Step by step explanation;

Using the lens formula; -1/u+1/v=1/f

rearranging, 1/v=1/18-1/27=1/54

hence 1/v=1/54.

To get the position of the image, V, find the reciprocal of 1/54.

Hence, v=54cm.

To obtain the size and nature of image,

use magnifcation formula; hi=V/u*h=54/-27*4=-8.0cm.

Therefore, size of image is 8cm.

Nature=virtual image.