Chapter 18.2, Problem 19PP

To determine

The position of the image by scale ray diagram.

Answer to Problem 19PP

The position of the image is $15\text{ cm}$ .

Explanation of Solution

Given:

The position of the object is $d_{\text{o}}=30.0\text{ cm}$ .

The focal length is $f=10.0\text{ cm}$ .

Calculation:

The procedure to draw the ray diagram is,

• Sketch the principal axis of the lens as a horizontal line.
• Place the lens at the center, placeC at the left side of the lens and place F at the other side.
• Sketch a vertical line at the lens point to represent the lens. This is the principal plane.
Sketch the object as an arrow and label its top $O_1$ .
• Draw ray 1, the parallel ray. It is parallel to the principal axis and reflects the principal plane and passes through F .
• Draw ray 2, the focus ray. It passes through F , reflects the principal plane, and is reflected parallel to the principal axis.
• The image is located where rays 1 and 2 cross after reflection. Label the point be $I_1$ .

Sketch the ray diagram as shown below.

  

The horizontal scale is 1 block is 1 cm.

The horizontal distance $\left(d_{\text{i}}\right)$ of the image from the lens is,

  $\begin{array}{c}{d}_{\text{i}}=\left(\begin{array}{l}\text{Number}\text{of}\text{blocks }\\ \text{from the lens in }\\ \text{horizontal direction}\end{array}\right)\text{×}\left(\text{Horizontal}\text{Scale}\right)\\ =15\text{blocks}\times 1.\text{0}\text{cm}\\ =\text{15}\text{cm}\end{array}$

Conclusion:

Thus, the position of image is $d_{\text{i}}=15.0\text{ cm}$ .