A convex mirror with a radius of curvature of 86.6 cm produces an image located 18.4 cm behind the mirror?

1. What is the focal length of this ­mirror?
2. Where is the object located?(Give a numeric answer)
3. Sketch a ray diagram using the three principle rays for this system.
4. Is the image upright or inverted?           
5. Is the image real or virtual?                     
6. Is the image large or smaller:                  
7. Where would you place an object to create a larger real image for a concave mirror with a focal length of 8cm?
8. Where would you put an object to create a larger imaginary image for a concave mirror with a focal length of 8cm?

Answer 1 -

Radius of curvature R = 86.6 cm

Focal length of mirror = f

f = - R/2

= - 86.6 / 2 = -43.3 cm

In a convex mirror, the focal point lies on the opposite side of the object, thus the focal length has a negative value.

Answer 2 -

Given in the question, d_i = -18.4 cm (as the image is located behind the mirror, so the image distance is assigned a negative sign)

According to the mirror equation, 1/f = 1/d₀ + 1/d_i

[ f= focal length; d₀ = object distance; d_i = image distance]

therefore,

d₀ = [(-43.3) (-18.4)] / [(-18.4) - (-43.3)] = 31.99 ~ 32 cm

Object distance d₀ = 32 cm

Answer 3 -

Answer 4 -

Magnification m = -d_i/d₀

or, m = - (-18.4/32) = 0.575

Since the value of magnification is positive, the image is upright.

Answer 5 -

As the image is formed behind a convex mirror, the image formed is virtual.

Answer 6 -

Since the value of magnification (0.575) is less than one, the image is smaller than the object.

Answer 7 -

To form an image in a concave mirror that is larger than the object and real, we have to place the object between focal point (or principal focus) and center of curvature. The image will be formed beyond the center of curvature.

Given focal length = 8 cm

Center of curvature = 2 x focal length = 2 x 8 = 16 cm

therefore, the object will have to be placed between 8 cm and 16 cm from the pole.

Answer 8 -

To form an image in a concave mirror that is larger than the object and imaginary, we have to place the object between the focal point (or principal focus) and the pole. The image will be formed behind the mirror.

Focal length = 8 cm

therefore, the object will have to be placed between 0 cm and 8 cm from the pole.

Please see the attached fie for the complete solution