Question

$h27_convexA$

The convex mirror shown in the drawing forms a virtual image of an arrow at x = x₂ = 17 cm. The image of the tip of the arrow is located at y = y₂ = 8.2 cm. The magnitude of the focal length of the convex mirror is 31 cm.

1.) What is x₁, the x co-ordinate of the object arrow?.

2) What is y₁, the y co-ordinate of the tip of the object arrow?

3) The object arrow is now moved such that image distance is halved, i.e., x_image,new = 8.5 cm. What is x_1,new, the new x co-ordinate of the object arrow?

4) What is y_2,new, the y co-ordinate of the image of the tip of the arrow when the x co-ordinate of the object arrow is equal to x_1,new?

5) Which of the following statements concerning a single convex mirror is false?

The image formed from any real object is always upright.

The image formed from any real object is always smaller than the object.

The image formed from any real object is always virutal and the magnitude of the image distance can be larger than the focal length of the mirror.

The image formed from a virtual object that is located inside the focal length of the mirror is real.

Answer 1

U = ? , v = 176 m, f = 31 cm i/f = 1/v-1/4 1/u = 1/v -1/f implies 1/17 -1/31 u = 527/14 = 37.64 c.m y2/y1 = v/u 8.2/y1 = 17/37.64 implies y1 = 18.155 cm v = 8.5 cm f = 31 cm u ? 1/31 = 1/8.5 -1/4 1/4 = 1/8.5 - 1/31 = 45/527 so u = 11.711 cm y2/y1 = v/u so y2 = 8.5/11.711 (18.155) = 13.177 cm