Question

A concave mirror forms a real image which is twice the size ofthe object. If the object is located 20 cm from the mirror, theradius os curvature must be about: a.) 13 cm b.) 20 cm c.) 27 cm d.) 40 cm

Answer 1

Answer: the correct answer is d.) 40 cm.

Explanation:

To find the radius of curvature of a concave mirror, we can use the mirror formula, which relates the object distance (u), the image distance (v), and the focal length (f) of the mirror.

The given information states that the concave mirror forms a real image that is twice the size of the object. This means that the magnification (M) is equal to 2.

The magnification is given by the formula:

M = -v/u

Since the magnification is positive in this case, we can rewrite the formula as:

M = v/u

Since the magnification is given as 2, we have:

2 = v/u

We also know that the object distance (u) is given as 20 cm.

Now, we can substitute these values into the mirror formula:

2 = v/20

Simplifying the equation:

v = 2 * 20

v = 40 cm

Now that we have the image distance, we can use the mirror formula to find the focal length (f) of the mirror.

The mirror formula is given by:

1/f = 1/v - 1/u

Substituting the values we have:

1/f = 1/40 - 1/20

1/f = (2 - 1)/40

1/f = 1/40

f = 40 cm

Therefore, the radius of curvature of the concave mirror is equal to the focal length, which is approximately 40 cm.