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two question

(1) A small fish, 0.40 m below the surface of a pond is viewed through a simple converging lens of focal length 3.0 m. The lens is kept at 0.20 m above the water surfaces such that the Fish lies on the optical axis of the lens. Find the location of the image of the Fish seen by the observer. The reflective index of water is 4/3.

(2) A luminous object is placed at a distance of 30 cm from a convex lens of focal length 20 cm. On the other side of lens, at what distance from the lens a convex mirror of radius of curvature 10 cm be placed so that image coincide with the object.


1. The "lens maker's equation" is 1/O + 1/i = 1/f. Since the lens is above the fish and the fish is on the optical axis of the lens, O equals the sum of the distances above and below the water, 0.6 m. The focal length, f, is 3.0 m. (You meant to say the refractive index of water is 4/3. It doesn't matter. Since the lens is vertically above the fish, light from the fish to the lens leaves the water at a 90 degree angle, so no refraction occurs. That appears to have been mentioned just to add confusion.)

So the equation is
1/0.6 m + 1/i = 1/3.0 m
1/i = 1/3.0 m - 1/0.6 m = 0.333 m^-1 - 1.667 m^-1 = -1.334 m^-1
Therefore i = 1/1.334 m = -0.75 m
The minus sign says that the image is on the virtual side.

2. I'm sorry. Combinations are beyond my area of expertise.

I hope this helps,


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Steve Johnson


I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.


I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University

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