Question

3. Two lenses with focal length 2 m are placed 4 m apart. An object is placed 1 m in front of the first lens. Where will its image appear relative to the second lens?1. -0.5 m2. 2/3 m3. -2 m4. 3 m

Answer 1

Given:

D1 = 2 m

D2 = 4 m

Distance between object and lens = 1 m

Let's find where the image will appear relative to the second lens.

To find the distance, apply the formula:

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

Thus, we have:

$\begin{gathered} \frac{1}{1}+\frac{1}{u}=\frac{1}{2} \\ \\ \frac{1}{u}=\frac{1}{2}-\frac{1}{1} \\ \\ \frac{1}{u}=-\frac{1}{2} \\ \\ u=-2\text{ m} \end{gathered}$

Now, we have the equation:

$\begin{gathered} v_2=L-f \\ \\ v_2=4--2 \\ \\ v_2=4+2 \\ v_2=6\text{ m} \\ \end{gathered}$

Now, let's use the Lens equation:

$\begin{gathered} \frac{1}{6}+\frac{1}{u_2}=\frac{1}{2} \\ \\ \frac{1}{u_2}=\frac{1}{2}-\frac{1}{6} \\ \\ \frac{1}{u_2}=\frac{3-1}{6}=\frac{2}{6} \\ \\ u_2=\frac{6}{2} \\ \\ u_2=3\text{ m} \end{gathered}$

Now, to find the image distance relative to the second lens, we have:

$-\frac{u_2}{v_2}=-\frac{3\text{ m}}{6\text{ m}}=-0.5\text{ m}$

Therefore, the image will appear -0.5 m relative to the second lens.

ANSWER:

1.) -0.5 m