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Chapter 31: Problem 13

A block of ice contains a hollow, air-filled space in the shape of a double- convex lens. Describe the optical behavior of this space.

Short Answer

Expert verified
As light passes through the air-filled, double-convex lens in the ice, it encounters a change in refractive index which causes the rays to refract, or bend, towards the central axis of the lens and converge to a point beyond the lens. This is due to the lens being thinner at the edges and thicker in the middle.

Step by step solution

01

The Nature of the Double-Convex Lens

The double-convex lens has two surfaces that are outwardly curved. It's characterized by curving outwards on both sides, creating a shape that's often compared to the side view of a lentil, which gives the lens its alternate name, converging lens.
02

Refraction in Different Media

When light passes from one medium to another with different refractive indices, it will change its speed and direction. In the case of the ice block, light will pass from ice (higher index of refraction) into the air-filled space (lower index of refraction), and then from air back into ice. This causes bending of the light rays, a phenomenon known as refraction.
03

Path of Light Through the Double-Convex Lens

Parallel rays of light entering the lens will be refracted twice. Once when entering the air-filled space from the ice, and again when entering back into the ice. With this lens shape, the rays will be refracted towards the central line, or principal axis, and will then converge at a focal point on the other side of the lens.

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Most popular questions from this chapter

A contact lens is in the shape of a convex meniscus (see Fig. 31.25). The inner surface is curved to fit the eye, with curvature radius \(7.80 \mathrm{mm} .\) The lens is made from plastic with refractive in\(\operatorname{dex} n=1.56 .\) If it has a \(44.4-\mathrm{cm}\) focal length, what's the curvature radius of its outer surface?

The refractive index of the human cornea is about \(1.4 .\) If you can see clearly in air, why can't you see clearly underwater? Why do goggles help?

Is the image on a movie screen real or virtual? How do you know?

Is there any limit to the temperature you can achieve by focusing sunlight?

For visible wavelengths, the refractive index of a thin glass lens is \(n=n_{0}-b \lambda,\) where \(n_{0}=1.546\) and \(b=4.47 \times 10^{-5} \mathrm{nm}^{-1} .\) If its focal length is \(30 \mathrm{cm}\) at \(550 \mathrm{nm}\), how much does the focal length vary over a wavelength spread of 10 nm centered on 550 nm?
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