Question

A 14 mm high object is 11 cm from a concave mirror with focal length 16 cm. Calculate (a) the location of the image, (b) the height of the image, and (c) the type of image.

Answer 1

(a) Focal length = f = - 16 cm ( concave mirror has negative focal length )

Object distance =u = - 11 cm, Image distance = v = ?

We know, ( 1 / f ) = ( 1 / v ) - ( 1 / u )

1 / v = 1 / f + 1 / u

v = uf / ( u + f ) = ( -11 ) x ( - 16 ) / ( - 11 - 16 )

v = - 6.52 cm

Hence, the image will be formed at a distance of 6.52 cm in front of the lens.

(b) Magnification = m = v / u = Image height / Object height

m = ( - 6.52 ) / ( - 11 ) = Image height / 14 mm

5.93 = Image height / 14 mm

Image height = 5.93 x 14 mm ~ 83 mm

Hence, height of the image is : 83 mm.

(c) Since, image distance is negative, the image is VIRTUAL.

Since, magnification is positive, the image is UPRIGHT.