In a retail store, a concave mirror with a radius of curvature of 80 cm is installed for security purposes. An object measuring 6 cm in height is placed 60 cm away from the mirror on the principal axis and perpendicular to it. Compute the magnification of the object's image formed by the mirror.+4-4+2-2
Question
In a retail store, a concave mirror with a radius of curvature of 80 cm is installed for security purposes. An object measuring 6 cm in height is placed 60 cm away from the mirror on the principal axis and perpendicular to it. Compute the magnification of the object's image formed by the mirror.+4-4+2-2
Solution
To solve this problem, we need to use the mirror formula and the magnification formula.
The mirror formula is 1/f = 1/v + 1/u, where f is the focal length, v is the image distance, and u is the object distance.
The magnification formula is m = -v/u, where m is the magnification, v is the image distance, and u is the object distance.
Step 1: Calculate the focal length The focal length (f) of a concave mirror is given by f = -R/2, where R is the radius of curvature. In this case, R = 80 cm, so f = -80/2 = -40 cm.
Step 2: Use the mirror formula to find the image distance (v) Substitute the values of f and u into the mirror formula: 1/f = 1/v + 1/u => 1/(-40) = 1/v + 1/(-60) => -1/40 + 1/60 = 1/v => v = -24 cm
Step 3: Use the magnification formula to find the magnification (m) Substitute the values of v and u into the magnification formula: m = -v/u => m = -(-24)/-60 = -0.4
So, the magnification of the object's image formed by the mirror is -0.4. The negative sign indicates that the image is inverted.
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