Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A lit slit and a screen stand apart on an optical bench, as in the picture. A convex lens gives a sharp image on the screen when its centre is at either of two places. The two places are apart. Find the focal length of the lens, the distance from the slit to the first position of the lens, and the magnification of the image at each position.
With the object and the screen apart, a lens that gives a sharp image at two positions apart has . The two magnifications are and , so . In a liquid, . With two different media, and .
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. and .
Plan. The displacement formula gives . The two positions come from and , and the magnifications from the positions.
Step 1. The focal length. .
Step 2. The positions. and from the slit.
Step 3. The magnifications. At the first position the object distance is and the image distance is , so . At the second position they swap, so .
Answer: , , and .
Check. , and . Also .
Watch out. The screen distance is more than , so two positions exist.
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