Question

a concave lens and a convex lens have same focal length 10cm are separated by 25cm. A point size objct is placed in front of convex les at 15 cm. Distance between object and final image



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Answer 1

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Class 12

>>Physics

>>Ray Optics and Optical Instruments

>>Combination of Mirror and Lenses

>>An object is placed 15cm in front of a c

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An object is placed 15cm in front of a convex lens of focal length 10cm . Find the nature and position of the image formed. Where should a concave mirror of radius of curvature 20 cm be placed so that the final image is formed at the position of the object itself?

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Solution

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Given: For convex lens u=−15cm f=10cm

To find: v

Solution: From lens formula

1v−

u

1

=

f

1

v

1

+

15

1

=

10

1

v

1

=

30

1

v=30cm

And magnification is =

−15

30

=−2

So for image is inverted and magnified and when a mirror is placed at a distance d behind lens then u for mirror is u

1

=−30+α

=α−30

and v=−30−14+α

From mirror formula

v

1

+

u

1

=

f

1

α−45

1

+

α−30

1

=

10

−1

(α−45)(α−30)

α−30+α−45

=

10

−1

(α−45)(α−30)

2α−75

=

10

−1

20α−750=−α

2

+75α−1350

α

2

=

−

+

(55)

2

−4/100

2

α=

2

55+−25

=40cm or 15cm

Hence d=15cm(as 40 cm not possible)