Question

I NEED HELP PLEASE, THANKS! :)

A 20.0 cm tall object is placed 50.0 cm in front of a convex mirror with a radius of curvature of 34.0 cm. Where will the image be located, and how tall will it be? Please show all work.

Answer 1

i = -12.7 cm; h = 5.07 cm

Step-by-step explanation:

1. Find the focal length

The focal length of a concave spherical mirror is half of its radius of curvature.

f = ½r = ½ × 34.0 cm = 17.0 cm

2. Find the image distance

A convex mirror produces a virtual image behind the mirror, so the image distance is negative.

`\begin{array}{rcl}(1)/(o) + (1 )/(i) & = & (1)/(f)\\\\(1)/(50.0) + (1 )/(i) & = & (1)/(-17.0)\\\\(1)/(i) & = & (1)/(-17.0) - (1)/(50.0)\\\\& = & (50.0 - (-17.0))/(500*(-17.0))\\\\& = & (67.0)/(-850)\\\\i & = & (-850)/(67.0)\\\\& = & \textbf{-12.7 cm}\\\end{array}`

3. Find the image size

`\begin{array}{rcl}\\\\\frac{h_{\text{i}}}{ h_{\text{o}}} & = & -(i)/(o) \\\\\frac{h_{\text{i}}}{ 20.0} & = & -(-12.7)/(50.0) \\\\h_{\text{i}} & = & 20.0 * (12.7)/(50.0)\\\\& = & \textbf{5.07 cm}\\\end{array}`