Chapter 7.4, Problem 17WE

To determine

To Find: the height of film shown in figure which is projected on a screen with $2.2\text{ m}$ tall screen image .

Answer to Problem 17WE

  $\text{0}\text{.55cm}$

Explanation of Solution

Given:

Figure is shown as.

  

  $LF=6\text{ cm and }LS=24\text{ m}$ .

Calculation:

In both triangles.

  $\begin{array}{l}\angle F=\angle S=90\therefore \left(\text{Right angle}\right)\\ \angle L=\angle L\therefore \left(\text{Common}\right)\end{array}$

Therefore, by AA postulate triangles are similar.

Ratio of sides of two similar triangle is equal.

  $\begin{array}{l}\frac{\text{Screen Imgae}}{\text{Height}\text{of}\text{Fim}\text{Image}}=\frac{LS}{LF}\\ \frac{2.2}{\text{Height}\text{of}\text{Fim}\text{Image}}=\frac{24}{6\times 0.01}\therefore \left(1\text{cm=0}\text{.01m}\right)\\ \text{Height}\text{of}\text{Fim}\text{Image}=\frac{2.2\times 6\times 0.01}{24}\\ \text{Height}\text{of}\text{Fim}\text{Image}=\text{0}\text{.0055m}\text{or}\text{0}\text{.55cm}\end{array}$

Therefore, the answer is $\text{0}\text{.55cm}$