Question

1. draw a ray diagram to show formation of an image in the example below. state the 4 characteristics of the image formed. (5 marks)
2. draw a ray diagram to show formation of an image in the example below. state the 4 characteristics of the image formed. (5 marks)
3. use this diagram to answer the following questions:

a) calculate the image distance. (3 marks)
b) calculate the image height. (3 marks)

Explanation:

Step1: Identify the mirror formula

The mirror formula is $\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$, where $u$ is the object - distance, $v$ is the image - distance, and $f$ is the focal length. For a spherical mirror, if the radius of curvature $R$ is known, $f=\frac{R}{2}$. From the diagram, the object distance $u = 4\ cm$ and assume it is a concave mirror with $f=- 2\ cm$ (negative for concave mirror).

Step2: Calculate the image distance $v$

Substitute $u = 4\ cm$ and $f=-2\ cm$ into the mirror formula $\frac{1}{4}+\frac{1}{v}=\frac{1}{-2}$. Then $\frac{1}{v}=\frac{1}{-2}-\frac{1}{4}=\frac{-2 - 1}{4}=\frac{-3}{4}$, so $v=-\frac{4}{3}\ cm\approx - 1.33\ cm$.

Step3: Identify the magnification formula

The magnification formula is $m =-\frac{v}{u}=\frac{h_i}{h_o}$, where $h_i$ is the image height and $h_o$ is the object height. Given $h_o = 2\ cm$.

Step4: Calculate the image height $h_i$

First, since $m =-\frac{v}{u}$, and $u = 4\ cm$, $v=-\frac{4}{3}\ cm$, then $m=-\frac{-\frac{4}{3}}{4}=\frac{1}{3}$. Also, since $m=\frac{h_i}{h_o}$ and $h_o = 2\ cm$, then $h_i=m\times h_o=\frac{1}{3}\times2=\frac{2}{3}\ cm\approx0.67\ cm$.

Answer:

a) The image distance is $-\frac{4}{3}\ cm$ (negative sign indicates the image is formed in front of the mirror).
b) The image height is $\frac{2}{3}\ cm$.