Question

A 2.30-cm-high object is situated 19.8 cm in front of a concave mirror that has a radius of curvature of 12.4 cm. Calculate (a) the location and (b) the height of the image.

Answer 1

Given,

Height of the object = h =2.30 cm

Object diatnace = o = -19.8 cm

radius of curvature = R = 12.4 cm

So f = R/2 = - 12.4/2 = 6.2cm

from the lents formula, we have

1/f = 1/o +1/i where i is the image dist. this gives us

i = of / (o - f) = (-19.8) (-6.2) / (-19.8 - (-6.2)) = -9.02 cm

If the lens eqn gives us a negative image distance then it means that the image is virtual and on the same side of the lens as object

(b)

h1/h = i/o, we get h1 = ixh/u = (-9.02)(2.30)/-19.8 = -1.04 cm

Image is going to be inverted.