A 6 cm tall object is placed at a distance 18 cm from a concave mirror. If the image formed is half the size of the object and is inverted, determine the focal length of the mirror.9 cm18 cm-6 cm-12 cm
Question
A 6 cm tall object is placed at a distance 18 cm from a concave mirror. If the image formed is half the size of the object and is inverted, determine the focal length of the mirror.9 cm18 cm-6 cm-12 cm
Solution
Given:
Height of the object, h1 = -6 cm (negative because the object is on the same side as the light being reflected)
Height of the image, h2 = -3 cm (negative because the image is inverted)
Object distance, u = -18 cm (negative according to the sign convention)
We need to find the focal length of the mirror.
We can use the mirror formula and magnification formula to solve this problem.
The mirror formula is 1/f = 1/v - 1/u, and the magnification formula is h2/h1 = -v/u.
First, we can find the image distance using the magnification formula:
-3/-6 = v/-18
v = -18 * (-3/-6) = -9 cm
Then, we substitute v = -9 cm and u = -18 cm into the mirror formula to find the focal length:
1/f = 1/-9 - 1/-18
1/f = -2/18 + 1/18
1/f = -1/18
Therefore, the focal length of the mirror is f = -18 cm.
Similar Questions
When an object of height 1 cm is kept at a distance 4 cm from a concave mirror, its erect image of height 1.5 cm is formed at a distance 6 cm behind the mirror. Find the focal length of mirror, by draw
An object 5 cm high is placed at a distance 60 cm in front of a concave mirror of focal length 10 cm. Find the position and size of the image by drawing.
In a concave mirror, an object is placed at a distance of 20 cm from the focus and the image is formed at a distance of 5 cm from the focus. What will be the focal length of the mirror?5 cm10 cm20 cm30 cm
An object is placed at 60 cm from the pole of a concave mirror with focal length of 20 cm. Find the distance at which the image is formed.
A makeup artist uses a concave mirror with a focal length of 12 cm to apply makeup with precision. If the client's face is positioned 24 cm from the mirror, how far is the image of the face located from the mirror's surface?-8 cm-24 cm+8 cm+24 cm
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.