Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
On an optical bench, a bright object reads cm from the lens and a sharp image on the screen reads cm from the lens. A check with a rod shows an index correction: the true object distance is cm more than the scale shows, and the true image distance is cm less than the scale shows. Find the corrected object and image distances, and the focal length of the lens. Say how far the uncorrected readings are from this value.
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.
Step 1. The corrections. cm. cm.
Step 2. The focal length. cm.
Step 3. The uncorrected value. cm, which is cm or too small.
Answer: cm, cm and cm.
Watch out. The correction is a fixed shift of the scale reading and it does not shrink with the distance. This is one more reason to take the focal length from a graph of many readings.
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Lens and mirror, real image: , so . Slab: , lateral shift , and apparent depth . Prism: , and at the least deviation.