A light bulb is placed 16.6 cm in front of a concave mirror. When the concave mirror is replaced by a plane mirror in the same location, the bulb's image moves 5.40 cm closer to the mirror. Calculate the focal length of the concave mirror.
i know that for plane mirrors distance of object=distance of image so i should just add 5.40 cm to 16.6 for di of the concave mirror, but it keeps saying my answer is wrong
To solve this problem, we can use the mirror formula for concave mirrors:
1/f = 1/do + 1/di
Where:
- f represents the focal length of the mirror
- do is the distance of the object from the mirror
- di is the distance of the image from the mirror
We are given that the object (light bulb) is placed 16.6 cm in front of the concave mirror. Let's assign this value to do: do = 16.6 cm.
We are also given that when the concave mirror is replaced by a plane mirror in the same location, the image moves 5.40 cm closer to the mirror. This means that the new distance of the image from the mirror is (16.6 cm + 5.40 cm) = 22 cm. Let's assign this value to di.
Substituting the known values into the mirror formula, we get:
1/f = 1/16.6 + 1/22
Now we can solve for f:
1/f = (22 + 16.6)/(16.6 * 22)
1/f = 38.6/(365.2)
f = 365.2 / 38.6
f ≈ 9.46 cm
So, the focal length of the concave mirror is approximately 9.46 cm.