# A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12 cm from P. At what point does the beam converge if the lens is - Physics

Numerical

A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12 cm from P. At what point does the beam converge if the lens is (a) a convex lens of focal length 20 cm, and (b) a concave lens of focal length 16 cm?

#### Solution

In the given situation, the object is virtual and the image formed is real.

Object distance, u = +12 cm

(a) Focal length of the convex lens, f = 20 cm

Image distance = v

According to the lens formula, we have the relation:

1/"v" - 1/"u" = 1/"f"

1/"v" - 1/12 = 1/20

1/"v" = 1/20 + 1/12

= (3 + 5)/60

= 8/60

∴ v = 60/8 = 7.5 cm

Hence, the image is formed 7.5 cm away from the lens, toward its right.

(b) Focal length of the concave lens, f = −16 cm

Image distance = v

According to the lens formula, we have the relation:

1/"v" - 1/"u" = 1/"f"

1/"v" = -1/16 + 1/12

= (-3 + 4)/48

= 1/48

∴ v = 48 cm

Hence, the image is formed 48 cm away from the lens, toward its right.

Concept: Refraction at Spherical Surfaces and Lenses - Refraction by a Lens
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#### APPEARS IN

NCERT Physics Part 1 and 2 Class 12
Chapter 9 Ray Optics and Optical Instruments
Exercise | Q 9.8 | Page 344
NCERT Class 12 Physics Textbook
Chapter 9 Ray Optics and Optical Instruments
Exercise | Q 8 | Page 346
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