Question

if an object 4 cm height is placed at a distance of 18 cm from concave mirror having focal length 12 cm.find the position, nature, and height of images​

Answer 1

Explanation:

Given:-

Object height ,ho = 4cm

Object distance ,u = -18cm

Focal length ,f = -12 cm

To Find:-

Position , nature & height of images.

Solution:-

According to the Question

Firstly we calculate the image distance of the object using mirror formula

• 1/v + 1/u = 1/f

where,

v is the Image Position

u is the object distance

f is the focal length

Substitute the value we get

:\implies:⟹ 1/v = 1/f - 1/u

:\implies:⟹ 1/v = 1/-12 - 1/(-18)

:\implies:⟹ 1/v = -1/12 + 1/18

:\implies:⟹ 1/v = -3+2/36

:\implies:⟹ 1/v = -1/36

:\implies:⟹ v = -36 cm

Hence, the image formed is 36 cm from the mirror .

Now, calculating the magnification of the image

m = hi/ho = -v/u

Substitute the value we get

:\implies:⟹ hi/4 = -36/-18

:\implies:⟹ hi/4 = 36/18

:\implies:⟹ hi/4 = 2

:\implies:⟹ hi = 8cm

Hence, the height of image is 8 cm

Nature of Image :- Real , inverted & larger than the object .