This works when you can neglect the spacing between the surfaces, that is, when

Question

This works when you can neglect the spacing between the surfaces, that is, when the radii are much bigger than the thickness of the lens. It is simple enough, but perilous for problems because of how the signs have to be interpreted. A lens surface that curves outward so that it is thicker at the center on that surface is "convex". One that curves inward, making it thinner at the center on that side, is concave. By convention, the sign of Y(R is positive if the lens is convex to the incoming light, and negative if it is concave. Here n is the index of refraction of the glass relative to the medium it is in (say air), and the (R)'s are the radii of the surfaces of the lens. Thinking of light as coming from the left, the radius is positive if it is convex to the left, concave to the right. For example, a lens that has convex surfaces on both sides with radii 10 cm, an index of 1.5, would have a focal length of f= 10 cm The second radius is negative because it is concave to the left and convex to the right. The shape of the surface and the index on both sides determine whether the lens converges the light, or diverges it 3. What would be the radius of curvature of the surfaces of a double convex lens with the same shape on both sides and a focal length of 1 meter? Assume an index of 1.5 4. Suppose you made a lens in which the first surface was convex to the left with a radius of 50 cm. Immediately after it the back surface is exactly the same, also convex to the left, with the same radius of curvature. Now take this lens outside and let sunlight fall on it. What happens to the light that goes through the lens? Explain it with these equations for a thin lens, and also with the wave theory of light.

Explanation / Answer

3.

using the lens maker's equation

1/f = (n - 1) (2/R)

given :

f = focal length = 1 m

n = 1.5

1/1= (1.5 - 1) (2/R)

R = 1 m

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