Question

1. Two students in a physics laboratory each have a concave mirror with the same radius of curvature, 52.0 cm. Each student places an object in front of a mirror. The image in both mirrors is two and a half times the size of the object. However, when the students compare notes, they find that the object distances are not the same. What is the distance of the farther object in cm?

I got 27.027 but that is incorrect

2. An object placed 27.0 cm in front of a convex mirror produces an image that is one-half the size of the object. What is the focal length of the mirror in cm ?(include the proper algebraic sign to reflect the nature of the mirror)

I got 34.01 but that is incorrect

Answer 1

1. For a concave mirror we get the magnified image for 3 cases.

a. When the object is placed between the pole and focus

b. Between Centre of curvature and principal focus

c. At the focus.

When the object is between the pole & focus the image is virtual & it won’t be obtained on a screen. Here both the students got the image. So one may be placed at the focus or the other may be placed between C & F. so the object distance is farther when it is placed between C & F. it can be calculated as follows.

Given R = - 52cm

F = R/2 = -52/2 = -26cm.

Magnification , m = -2.5 , for real image magnification is –ve.

We have , m = -v/u , -2.5 = -v/u , v = 2.5u

F = uvu+v , -26 = ux2.5uu+2.5u , -26 = 2.5u23.5u , -26 x 3.5 = 2.5u

U = -26x3.52.5 = - 36.4cm.

2. Given , u = -27cm

m = 0.5 , since convex mirror forms virtual image m is positive.

F = ?

We have m = -v/u , 0.5 = -v/u , v = - 0.5u = - 0.5 x – 27 = 13.5cm.

F = uvu+v = -27 x 13.5-27+13.5 = 364.513.5 = 27cm.