Question

Marooned on a desert island and with a lot of time on your hands, you decide to disassemble your glasses to make a crude telescope with which you can scan the horizon for rescuers. Luckily you’re farsighted, and, like most people, your two eyes have different lens prescriptions. Your left eye uses a lens of power $+4.5D$and your right eye’s lens is $+3.0D$. a. Which lens should you use for the objective and which for the eyepiece? Explain.

b. What will be the magnification of your telescope?

c. How far apart should the two lenses be when you focus on distant objects?

Short answer

a. $(D=3)$right eye lens use as objective.

b. The magnification of the telescope is $M=1.5$.

c. The two lenses are$L=0.55$.

Step-by-step solution

Part(a) Step 1: Given Information.

We need to find out which lens is use for the objective and which for the eyepiece.

part (a) step 2: Explanation

Objective lenses have large diameters because larger lens to collect more light and we an see finder object . Collects the parallel rays from a distant object. Where $(D=3)$right eye lens used as an objective.

part (b) Step 1: Given Information.

We need to find out the magnification of the telescope.

Part (b) Step 2: Simply.

Magnification of the telescope:

$$\begin{gathered} M=\frac{f_{obj}}{f_{eye}} \\ M=\frac{0.33}{0.22} \\ M=1.5 \end{gathered}$$.

Part (c) Step 1: Given Information.

We need to find out what will be the distance between the two lenses be when we focus on distant objects.

Part (c) Step 2: simply.

Distance between eyepiece and objective lens slightly less than the sum of the focal length.

$$\begin{gathered} L\le f_R+f_L \\ L=0.33+0.22 \\ L=0.55 \end{gathered}$$.