Question

Geometric Optics - A convex spherical mirror has a radius of magnitude R and is centered at C. A real object R/4 tall is located a distance 1 R to the left of the mirror's vertex. Draw a ray diagram showing the formation of the image, and compute the magnification and image location for the object. - show both sketch and calculations

Answer 1

Using lens equation

1/f = 1/object distance + 1/image distance

for convex spherical mirror, f = negative

as we know f = R/2

-2/R = 1/1R + 1/image distance

1/image distance = -2/R - 1/1R

image distance = -R/3

Magnification = -image distance / object distance

magnification = -R/3 / R

magnification = 0.333

since magnification is positive , image will be upright.

Height of image = m * height of object = 0.333 * R/4 = 0.08325R (smaller than object)

Here is a rough sketch (not to scale)