Chapter 34: Q. 34 (page 991)

A $1.0 - c m$ -tall object is $75 c m$ in front of a converging lens that has a $30 c m$ focal length.
$(a)$ Use ray tracing to find the position and height of the image. To do this accurately, use a ruler or paper with a grid. Determine the image distance and image height by making measurements on your diagram.
$(b)$ Calculate the image position and height. Compare with your ray-tracing answers in part $a$ .

Short Answer

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Part $(a)$

$(a)$ The image distance is localid="1649234286834" $s^{'} = 50 c m$ and image height islocalid="1649234293008" $h^{'} = 0.67 c m .$

Part $(b)$

$(a)$ The image distance is $s^{'} = 50 c m$ and image height is $h^{'} = 0.67 c m .$

The both part agrees.

Step by step solution

Step: 1 Finding lateral magnification:

From thin lens equation,

$\frac{1}{s} + \frac{1}{s^{'}} = \frac{1}{f}$

The convex lens of focal lens is positive and concave lens is negative:the image virutal is negative and real image distance is positive.

The lateral magnification is

$| M | = \frac{image height}{object height} = \frac{h^{'}}{h} M = - \frac{s^{'}}{s}$

object height is $h = 1.0 c m .$

The lens is converging.

The distance lens object is $s = 75 c m .$

The focal length is $f = 30 c m .$

Step: 2 Finding image distance: (part a)

From lens equation is

$\begin{array}{l} \frac{1}{s} + \frac{1}{s^{'}} = \frac{1}{f} \\ \frac{1}{s^{'}} = \frac{1}{f} - \frac{1}{s} \\ \frac{1}{s^{'}} = \frac{s - f}{s f} \\ s^{'} = \frac{s f}{s - f} \\ s^{'} = \frac{(75 cm) (30 cm)}{75 cm - 30 cm} \\ s^{'} = 50 cm . \end{array}$

The ray trace diagram is

Step: 3 Finding image height: (part b)

The lateral magnification lens by

$\begin{array}{l} M = - \frac{s^{'}}{s} \\ M = - \frac{50 cm}{75 cm} \\ M = - \frac{2}{3} . \\ \begin{array}{l} | M | = \frac{h^{'}}{h} \\ h^{'} = h | M | \\ h^{'} = (1.0 cm) (\frac{2}{3}) \\ h^{'} = 0.67 cm . \end{array} \end{array}$

By comparing, the both parts are agree.

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Short Answer

Step by step solution

Step: 1 Finding lateral magnification:

Step: 2 Finding image distance: (part a)

Step: 3 Finding image height: (part b)

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