Question

the image of an object formed by a lens is of magnification -1 if the distance between the object and its image is 60 cm what is the focal length of the lens? if the object is moved 20 cm towards the lens where would the image be formed? state the reasons and also draw the diagram in support of your answer

Answer 1

magnification, m = -1 = v/u

[ here magnification is negative. it means lens must be convex lens. ]

or, v = -u .........(1)

a/c to question,

v + (-u) = 60cm ..........(2)

from equations (1) and (2),

-u -u = 60cm

or, -2u = 60cm

or, u = -30cm

v = 30cm

use lens maker formula, 1/v - 1/u = 1/f

or, 1/30 - 1/-30 = 1/f

or, 1/60 = 1/f => f = 60cm

again, if the object is moved 20cm towards the lens .

u = -(30 - 20) = -10cm

f = +60cm

use lens maker formula, 1/v - 1/u = 1/f

or, 1/v - 1/(-10) = 1/60

or, 1/v = 1/-10 + 1/60 = (-6 + 1)/60

or, v = -12cm

hence, image is formed left side of lens.

Answer 2

Answer:

Given m=−1,

since m=v/u=−1 , -ive sign shows that v is +ive i.e. image is formed on the other side of lens , and

∣v∣=∣u∣

now distance between object and image =60cm ,

or ∣u∣+∣v∣=60

or ∣u∣+∣u∣=60

or ∣u∣=60/2=30cm or u=−30cm

and ∣v∣=30cm or v=30cm

now by lens formula ,

f=uv/(u−v)=

−30−30

−30×30

=15cm (+ive focal length means it is a convex lens) .

Now if u=−30+20=−10cm , as u(10cm)<f(15cm) ,it means object lies between F and C , in this position of object the rays from object cannot meet at any point on the other side of lens ,which is also clear from the position of image found below ,

From lens equation v=

u+f

uf

=

−10+15

−10×15

=−30cm ,

-ive sign shows that image will be formed on the same side of lens , where the object is placed .

hope this help you

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