Example 9.3 An object is placed at 0 10 cm. h) 5 em in front of aconca

1.	Example 9.3 An object is placed at 0 10 cm. h) 5 em in front of aconcave mirror of radius of curvature 15 cm. Find the position, natureand magnification of the image in each case
Answer» 1) Object distance = 10 cmObject distance =u = -10 cmRadius of curvature = R = -15 cm Focal length = ff = 2R so,f = R/2 = -15/2 cm We know that :-1/v + 1/u = 1/f v = image distance 1/v = 1/f - 1/u = 1 / (-15/2) - (-1/10) = -2/15 + 1/10 = -4/30 + 3/30 = -1/30 1/v = -1/30v = -30 cmImage distance = v = -30 cm The position of image is 30 cm in front of mirror. we know that ,magnification , m = -v/u = -(-30)/-10 = -3 Nature :-This negative sign indicates that the image is real ,and inverted. ii) Object distance = 5 cm Object distance = u = -5cmFocal length = -15/2 cm 1/v = 1/f - 1/u = -2/15 - (-1/5) = -2/15 + 1/5 = 1/15 v = 15 cmImage distance = v = 15 cm we know ,m = -v/u = -15/-5 = 3 Nature of image :- The positive sign of magnification indicates that the image is virtual , erect and magnified right answer

Example 9.3 An object is placed at 0 10 cm. h) 5 em in front of aconcave mirror of radius of curvature 15 cm. Find the position, natureand magnification of the image in each case

Answer»

1) Object distance = 10 cmObject distance =u = -10 cmRadius of curvature = R = -15 cm

Focal length = ff = 2R

so,f = R/2 = -15/2 cm

We know that :-1/v + 1/u = 1/f

v = image distance

1/v = 1/f - 1/u = 1 / (-15/2) - (-1/10) = -2/15 + 1/10 = -4/30 + 3/30 = -1/30

1/v = -1/30v = -30 cmImage distance = v = -30 cm

The position of image is 30 cm in front of mirror.

we know that ,magnification , m = -v/u = -(-30)/-10 = -3

Nature :-This negative sign indicates that the image is real ,and inverted.

ii) Object distance = 5 cm

Object distance = u = -5cmFocal length = -15/2 cm

1/v = 1/f - 1/u = -2/15 - (-1/5) = -2/15 + 1/5 = 1/15

v = 15 cmImage distance = v = 15 cm

we know ,m = -v/u = -15/-5 = 3

Nature of image :- The positive sign of magnification indicates that the image is virtual , erect and magnified

right answer