Question

Use the mirror equation to show that
(i) An object placed between f and 2f of a concave mirror produces a real image beyond 2f.
(ii) A convex mirror always produces a virtual image independent of the location of the object.
(iii) An object placed between the pole and focus of a concave mirror produces a virtual and enlarged image.

Answer 1

Brainly.in

1

Secondary SchoolPhysics 10 points

Use the mirror equation to deduce that: (a) an object placed between f and 2 f of a concave mirror produces a real image beyond 2 f. (b) a convex mirror always produces a virtual image independent of the location of the object. (c) the virtual image produced by a convex mirror is always diminished in size and is located between the focus and the pole. (d) an object placed between the pole and focus of a concave mirror produces a virtual and enlarged image.[Note: This exercise helps you deduce algebraically properties of images that one obtains from explicit ray diagrams]

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prmkulk1978

prmkulk1978 Ace

a) Mirror Formula : 1/v+1/u=1/f

For concave mirror:

f<0, as object always placed on the left side of mirror so u<0

According to question:

f<u<2f [ object lies between f and 2f]

1/2f>1/u>1/f

or

-1/2f<-1/u< -1/f

add 1/f on both sides :

1/f-1/2f< 1/f-1/u<0------------(1)

From lens formula : 1/f=1/v-/1u

we get : 1/2f <1/v

or v>2f

as f is negative , 2f is also negative and hence v will be also negative.

Nature of image : Real and lies between beyond 2f

b)For convex mirror :

f is positive

f>0 and u<0

from lens formula : 1/v =1/f-1/u

as f>0 and u<0

value 1/v >0 or v>0 or v is always positive.

The image formed is virtual . It does not depend on location of object.

c) For convex mirror f>0, u<0

from lens formula : 1/v=1/f-1/u

1/v>1/f or v<f