Lecture 15Refraction, Lenses, Aberrations

Chapter 23.4 23.7

Outline

• Atmospheric Refraction• Thin Lenses• Aberrations

Atmospheric RefractionAtmospheric refraction is bending of light due to gradual changing density of the air throughout the atmosphere.Images of objects, close to the horizon, appear at a higher elevation that the real objects are.

Atmospheric refraction is hardly noticeable at high viewing angles (e.g., near zenith).

Atmospheric Refraction

MiragesThe mirage is an atmospheric refraction phenomenon due to large temperature changes of the air at different heights above the Earth.

There are superior (inverted image above the ‘normal’) and inferior (inverted image is below the ‘normal’).

Light rays from an object move toward the observer in two different ways through the different temperature layers.

Thin Lenses

A lens is a piece of glass (plastic) with two refracting surfaces, which are either curved (e.g., a segment of a sphere) or plain.

Lenses are used to form images by refraction in optical instruments (microscopes, telescopes, cameras, etc.)

Two types of lenses: converging (thickest in the middle) and diverging (thickest at the edges).

Thin Lenses

The focal length of a lens is the image distance of an object at an infinite distance from it.The focal point is where a group of rays parallel to the lens’ axis converges.

The thin-lens equation has the same form as the mirror equation.

1 1 1 + = p q f

1 1 1 = (n1) F R1 R2

Lens maker’s equation

Sign Convention

Ray Diagram for Thin Lenses

Ray 1: parallel to the lens’ axis, to its center, through the focus on the other lens’ side.Ray 2: through the lens’ center, continues in a straight line.Ray 3: through the closest focus, emerging from the lens parallel to the lens’ axis.

Combinations of Thin Lenses

For a system of two lenses, the image formed by the first one is treated as the object for the second one.The image formed by the second lens is the final image of the system.The overall magnification is the product of the magnifications of the individual lenses.

Problem with a Two-Lens System

Problem: Find the image location.

Solution: p' = 12cm f '= 6cm

1 1 1 = f ' p' q'

q' = 4cm

p = 12+4=16cm

f = 8cm

1/q = 1/81/16=1/16q = 16cm

image

Aberrations

Departures of real images from the ideal predicted by simple theory are called aberrations.

Types of aberrations

To reduce spherical aberration, parabolic mirrors are used instead of spherical.To reduce chromatic aberration, combinations of converging and diverging lenses are used.

Summary

• Atmospheric refraction is a phenomenon that moves images of objects, seen through the air, due to a gradual change of the air density and temperature.

• Thin lenses are used to form images by refraction in optical instruments to enhance our vision.

• Aberrations are distortions of images, predicted by the simple theory of geometric optics.