Question

A concave mirror (f₁ =13.2 cm) and a convex mirror (f₂ =−6.00 cm) are facing each other and are separated by a distance of 34.2 cm. An object is placed between the mirrors and is 17.1 cm from each mirror. Consider the light from the object that reflects first from the concave mirror and then from the convex mirror. What is the distance of the image (di,2) oroduced by the convex mirror?

Answer 1

The distance of the image produced by the convex mirror is -13.7 cm.

Step-by-step explanation:

To find the distance of the image produced by the convex mirror, we need to consider the light from the object that reflects first from the concave mirror and then from the convex mirror. The concave mirror has a focal length of 13.2 cm and the convex mirror has a focal length of -6.00 cm. The object is placed between the mirrors and is 17.1 cm from each mirror.

Using the mirror formula, 1/f = 1/do + 1/di, we can determine the image distance di for the concave mirror and the object distance do for the convex mirror. The image distance di for the concave mirror is given by di = 1 / (1/f₁ - 1/do). Plugging in the values, di = 1 / (1/13.2 - 1/17.1). Solving for di gives di = 7.38 cm. Now, we can use this value of di as the object distance for the convex mirror and solve for the image distance di,2 using di,2 = 1 / (1/f₂ - 1/di). Plugging in the values, di,2 = 1 / (1/-6.00 - 1/7.38). Solving for di,2 gives di,2 = -13.7 cm.