An object is placed 5.0 cm from front of a concave spherical mirror of focal length 20 cm. what type of image would you expect?
To determine the type of image formed by a concave spherical mirror, you can use the mirror formula:
1/f = 1/v - 1/u
where:
- f is the focal length of the mirror,
- v is the image distance (distance of the image from the mirror), and
- u is the object distance (distance of the object from the mirror).
Given:
f = -20 cm (for a concave mirror, the focal length is negative),
u = -5.0 cm (since the object is placed in front of the mirror, the object distance is also negative).
Substituting these values into the mirror formula, we can solve for v:
1/-20 = 1/v - 1/-5.0
Simplifying, we get:
-1/20 = 1/v + 1/5.0
Now, let's solve for v:
Multiply through by 20v and 5.0v to eliminate fractions:
-5v = 20 + 4v
Combine like terms:
-9v = 20
Divide both sides by -9:
v ≈ -2.22 cm
The negative sign indicates that the image is formed on the same side of the mirror where the object is placed. This implies that the image is a virtual image.
Therefore, for an object placed 5.0 cm in front of a concave spherical mirror with a focal length of 20 cm, a virtual image is expected to be formed.