Chapter 18.2, Problem 20PP

To determine

The location and height of image using ray diagram.

Answer to Problem 20PP

The location of the image is $-15.0\text{ cm}$ .

The height of the image is $1.5\text{ cm}\left(\text{erect}\right)$ .

Explanation of Solution

Given:

The height of the object is $h_{\text{o}}=1.0\text{ cm}$ .

The object is located at a distance of $10\text{ cm}$ from the lens.

The focal length is $f=30.0\text{ cm}$

Calculation:

The procedure to draw the ray diagram is,

• Sketch the principal axis of the mirror as a horizontal line.
• Place the mirror at the center, place C at the left side of the mirror and place F at the other side.
• Sketch a vertical line at the mirror point to represent the mirror. 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 as $I_1$ .

Sketch the ray diagram as shown below.

  

The horizontal scale of 1 block is $2.0\text{ cm}$ .

The vertical scale of 1 blocks is $\left(\frac{1}{3}\right)\text{ cm}$ .

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

  $\begin{array}{c}{d}_{\text{i}}=-\left(\begin{array}{l}\text{Number}\text{of}\text{blocks }\\ \text{from the lens in }\\ \text{horizontal direction}\end{array}\right)\text{×}\left(\text{Horizontal}\text{Scale}\right)\\ =-7.5\text{blocks}\times 2.\text{0}\text{cm}\\ =-\text{15}\text{cm}\left(\begin{array}{l}\text{negative sign indicates image}\\ \text{is formed in front of the lens}\end{array}\right)\end{array}$

The vertical height $\left(h_{\text{i}}\right)$ of the image is,

  

Conclusion:

Thus, the location of the image is $-15.0\text{ cm}$ .

Thus, the height of the image is $1.5\text{ cm}\left(\text{erect}\right)$ .