Question

A small object is placed in front of a converging mirror with radius \(R=7.50 \mathrm{~cm}\) so that the image distance equals the object distance. How far is this object from the mirror? a) \(2.50 \mathrm{~cm}\) b) \(5.00 \mathrm{~cm}\) c) \(7.50 \mathrm{~cm}\) d) \(10.0 \mathrm{~cm}\) e) \(15.0 \mathrm{~cm}\)

Short answer

a) 3.75 cm b) 5.00 cm c) 7.50 cm d) 15.0 cm Answer: c) 7.50 cm

Step-by-step solution

Write down the mirror equation

The mirror equation is: (1/d_o) + (1/d_i) = (1/f) where d_o is the object distance, d_i is the image distance, and f is the focal length of the mirror.

Find the focal length using the radius of curvature

The focal length of a mirror is half the radius of curvature, so we can calculate the focal length (f) as: f = R/2 = 7.50 cm / 2 = 3.75 cm

Set object distance equal to image distance

Since the image distance is equal to the object distance, we can write: d_o = d_i

Apply the mirror equation

Now, we can plug this information into the mirror equation: (1/d_o) + (1/d_o) = (1/3.75 cm) Combine the terms on the left side of the equation: (2/d_o) = (1/3.75 cm)

Solve for the object distance

Now, we can solve for d_o: d_o = 2/ (1/3.75 cm) = 2 * 3.75 cm = 7.50 cm The correct answer is (c). The object is 7.50 cm away from the mirror.