Question

A 3.0 cm lighted candle is placed 20 cm from a concave spherical mirror with a radius of curvature of 30 cm.(a)Where should a screen be placed (in cm) in order to see the candle's image clearly? (Give your answer as a distance from the center of the mirror.) cm(b)What is the minimum height (in cm) of the screen in order to see the candle's complete image? cm

Answer 1

Given:

The object's height is h = 3 cm

The object's distance from the concave mirror is u = -20 cm

The radius of curvature is R = - 30 cm

Required:

(a) Image's distance from the mirror

(b) Image's height

Explanation:

The focal length of the mirror can be calculated as

$\begin{gathered} f=\frac{R}{2} \\ =-\frac{30}{2} \\ =-15\text{ cm} \end{gathered}$

(a) The image's distance can be calculated using the mirror formula as

$\begin{gathered} \frac{1}{v}+\frac{1}{u}=\frac{1}{f} \\ \frac{1}{v}=\frac{1}{f}-\frac{1}{u} \\ =\frac{1}{-15}-\frac{1}{-20} \\ v=-60\text{ cm} \end{gathered}$

(b) The image's height can be calculated as

$\begin{gathered} \frac{h^{\prime}}{h}=-\frac{v}{u} \\ h^{\prime}=-\frac{v}{u}\times h \\ =\frac{-(-60)}{-20}\times3 \\ =-9\text{ cm} \end{gathered}$

Final Answer:

(a) Image's distance from the mirror is v = -60 cm

(b) Image's height is h' = -9 cm