Chapter 34: Q. 31 (page 991)

A $1.0 - c m -$ tall candle flame is $60 c m$ from a lens with a focal length of $20 c m$ . What are the image distance and the height of the flame's image?

Short Answer

Expert verified

The distance image is $S^{'} = 30 c m$ and the flames's image height is $h^{'} = 0.5 c m .$

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

localid="1649225203836" $| M | = \frac{image height}{object height} = \frac{h^{'}}{h} M = - \frac{s^{'}}{s} .$

The candle height flame is localid="1649225208567" $h = 1.0 c m .$

The candle flame distance to the lens is localid="1649225213777" $s = 60 c m .$

The focal lens length is localid="1649225220303" $f = 20 c m .$

Step: 2 Finding image flame's distance:

By thin lens equation,

$\begin{array}{l} \frac{1}{s} + \frac{1}{s^{'}} = \frac{1}{f} \\ \frac{1}{s^{'}} = \frac{1}{f} - \frac{1}{s} \\ \frac{1}{s^{'}} = \frac{s - f}{s f} \\ s^{'} = \frac{s f}{s - f} \\ s^{'} = \frac{(60 cm) \times (20 cm)}{60 cm - 20 cm} \\ s^{'} = 30 cm . \end{array}$

Step: 3 Finding image height:

The lateral magnification lens by

$\begin{array}{l} M = - \frac{s^{'}}{s} \\ M = - \frac{30 cm}{60 cm} \\ M = - 0.5 . \end{array} \begin{array}{l} | M | = \frac{h^{'}}{h} \\ h^{'} = h | M | \\ h^{'} = (1.0 cm) (0.5) \\ h^{'} = 0.5 cm . \end{array}$

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A $1.0 - c m -$ tall candle flame is $60 c m$ from a lens with a focal length of $20 c m$ . What are the image distance and the height of the flame's image?

Short Answer

Step by step solution

Step: 1 Finding lateral magnification:

Step: 2 Finding image flame's distance:

Step: 3 Finding image height:

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A 1.0-cm-tall candle flame is 60cmfrom a lens with a focal length of 20cm. What are the image distance and the height of the flame's image?

Short Answer

Step by step solution

Step: 1 Finding lateral magnification:

Step: 2 Finding image flame's distance:

Step: 3 Finding image height:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electricity

Linear Momentum

Measurements

Astrophysics

Nuclear Physics

Oscillations

Study anywhere. Anytime. Across all devices.

A $1.0 - c m -$ tall candle flame is $60 c m$ from a lens with a focal length of $20 c m$ . What are the image distance and the height of the flame's image?