Prove, in the case of a convex mirror, that 1 v - 1 u = 2 r = 1 f .

Let AB be an object lying on the principle axis of the convex mirror of small aperture. Virtual image is behind the mirror A'B'. Draw LN perpendicular to the principle axis. Now ∆ NLF and A'B'F are similar. Therefore, A ' B ' N L = A ' F N F Since aperture is small, point N lies very close to P. So, N F = P F , L N = A B Also, ∆ ABC and A'B'C are similar, so, A ' B ' A B = A ' C A C = P C - P A ' P A + P C So we get, P F - P A ' P F = P C - P A ' P A + P C . . . . . . ( i ) From diagram, P A ' = v P F = f P C = R = 2 f P A = u (without any sign convention) So, equation (i) becomes, f - v f = 2 f - v u + 2 f ⇒ 2 f 2 - v f = u f - u v + 2 f 2 - 2 v f ⇒ u v = u f - v f Dividing by u v f , we get, 1 f = 1 v - 1 u .

E M B I B E

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 12 - Reflection of Light>EXERCISE 12>Q 1

EASY

12th West Bengal Board

IMPORTANT

Earn 100

Show that a beam of rays from a point source after reflection at a plane mirror appears to diverge from another point. What is the point called? What is its nature?

Important Questions on Reflection of Light

MEDIUM

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 12 - Reflection of Light>EXERCISE 12>Q 2

Explain, with diagram, how a plane mirror produces an image. Prove that the image is as far back of the mirror as the object is in front of it.

MEDIUM

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 12 - Reflection of Light>EXERCISE 12>Q 3

Explain, with a neatly drawn diagram how two plane mirrors inclined at right angles to each other form images of an object placed between them.

MEDIUM

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 12 - Reflection of Light>EXERCISE 12>Q 7

Prove, with the help of a diagram, that a mirror of minimum length must be hung at a definite position in the wall in order that a man can see his full image.

MEDIUM

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 12 - Reflection of Light>EXERCISE 12>Q 8

A man stands at the centre of a room. A plane mirror hangs on the wall in front of him. Show that the minimum height of the mirror through which the man can see the full image of the wall behind him is one-third the height of the wall.

MEDIUM

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 12 - Reflection of Light>EXERCISE 12>Q 10

Prove, in the case of a convex mirror, that

\frac{1}{v} - \frac{1}{u} = \frac{2}{r} = \frac{1}{f}

.

HARD

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 12 - Reflection of Light>EXERCISE 12>Q 11

Establish the relation connecting object distance, image distance and focal length of a spherical mirror. Show that the ratio of the length of the image formed by a concave mirror to the length of the object is equal to the ratio of their respective distances from the mirror.

MEDIUM

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 12 - Reflection of Light>EXERCISE 12>Q 12

Explain with neat diagram the formation of image of an extended object by reflection from a convex mirror. Obtain a relation between the object distance, image distance and the focal length of the mirror.

HARD

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 12 - Reflection of Light>EXERCISE 12>Q 13

How will you proceed to determine the focal length of a convex mirror ?