Chapter 17, Problem 67A

To determine

The image position and image height for the object.

Answer to Problem 67A

The image position is 33 cm.

Image height is 4.04 cm.

Explanation of Solution

Given:

The given image is

  

The focal length of the concave mirror, $f=16.0\text{cm}$

The height of the object, $h_o=3.8\text{cm}$

The object distance from the mirror, $d_o=31\text{cm}$

Formula used:

Mirror equation,

  $\frac{1}{f}=\frac{1}{d_i}+\frac{1}{d_o}$

Where,

  $\begin{array}{l}f=\text{focal length}\\ d_i=\text{ image distance}\\ d_o=\text{object distance}\end{array}$

And,

Magnification, $\frac{h_i}{h_o}=-\frac{d_i}{d_o}$

Where,

  $\begin{array}{l}{h}_i=\text{image height}\\ h_o=\text{object height}\end{array}$

Calculation:

Using the given values in Mirror equation, the image distance will be,

  $\begin{array}{c}\frac{1}{f}=\frac{1}{d_i}+\frac{1}{d_o}\\ \frac{1}{16}=\frac{1}{d_i}+\frac{1}{31}\\ d_i=\frac{31\times 16}{31-16}\\ \approx 33.0\text{cm}\end{array}$

Then, the image height will be,

  $\begin{array}{c}\frac{h_i}{h_o}=-\frac{d_i}{d_o}\\ \frac{h_i}{3.8}=-\frac{33.0}{31}\\ h_i=-4.04\text{cm}\end{array}$

Negative sign denotes inverted image

Conclusion:

Therefore, the image of robin is formed at a distance of $33.0\text{cm}$ from the mirror and his image height is $4.04\text{cm}$ .