Question

An object, 7cm is size, is placed at 27cm in front of a concave mirror of focal length 18cm. At what distance from the mirror should be a screen be placed in order to obtain a sharp image? Find the nature and the size of the image. ​

Answer 1

Answer:

Given

Focal length of concave mirror (f)= -18cm

Conventionally concave mirror and concave lens have negative focal lengths and convex mirror and convex lens have positive focal lengths. The co-ordinate system is taken with respect to the Pole as origin. All distances are measured from the pole and distance measured in the direction of light rays are positive and opposite to the direction are considered as negative. Distances above the principal axis are positive and vice-versa. Following these conventions

Object distance (u)= -27cm

Object height= 7cm

Let image distance be v cm

We know by mirror formula that

1/v + 1/u = 1/f

1/v + 1/(-27) = 1/(-18)

1/v = 1/(-18) + 1/27

1/v= (-3+2)/54

1/v= -1/54

v= -54 cm

Thus, placing a screen at a distance of 54 cm from the concave mirror on the same side as object will give us a sharp and focused image.

The magnification will be

m= -v/u

m= -(-54)/(-27)

m= -2

|m|>1 => enlarged image and the negative sign implies that the image is inverted

m can also be written as

m= Height of image/ Height of object

-2= Height of image/7

Height of image= -14cm

Thus the image has a height of 14 cm and is inverted and present at a distance of 54 cm from the mirror.

Answer 2

Answer:

We know that, for a concave mirror the focal length will be negative.

Therefore, given: u = -27cm f = -18cm h(object size) = 7cm

( Note that the distance at which you will obtain sharp image will be your "v" i.e. the object distance for that image formation which is required in the question)

hence,

1/v + 1/u = 1/f (mirror formula)

1/v + (1/(-27)) = 1/(-18)

1/v = 1/27 + 1/-18 ( LCM of 18 and 27 is 54)

1/v = 1/(-54)

v = -54cm

image distance = -54cm

hence, image is formed on the same side.

now we know,

h'/h = -v/u (h' denotes object height)

h'/7 = -(-54)/-(27)

h' = 7 * (-2)

h' = -14cm

hence, image is inverted (since h' is negative) and it is on the same side of that of the object (since v is negative).

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