Question

16) An object 0.600 cm tall is placed 16.5 cm to the left of the vertex of a concave spherical mirror having a radius of curvature of 22.0 cm. Determine how tall the image is in cm, and type the word real or virtual in the unit box indicating the nature of the image.

Answer 1

Given,   object distance (u) = 16.5 cm

                Radius of convex mirror (R) = 22 cm

                Height of the object (h_o) = 0.6 cm

Let,        image distance be ‘v’

                Image height be ‘h_i’

We know that, mirror equation is given by          1/u +1/v = 1/f

                Where, f is the focal length of the mirror given by f = R/2 = 11 cm

                By convention as we are measuring the distances of object and focal length opposite to the light ray direction they are taken to be negative. If it is along the direction of light ray it is positive which is not the case here.

                i.e. u = -16.5 ,f = -11 should be substituted in mirror equation.

                1/v = 1/16.5 – 1/11

                1/v = 1/33

                v = 33 cm

We know that, magnification of image (M) = -v/u = h_i/h_o

                h_i/h_o = -(-33/-16.5)

                h_i/h_o = -2 , |M|> 1 that is the image is magnified.

                h_i = -2h_o

                h_i = -1.2 cm, as height of image is negative it implies that it is an inverted with respect to object.

Therefore, Image formed is 1.2 cm tall. It is real, inverted and magnified.