Lecture 15 Optical Instruments

LECTURE 15 OPTICAL INSTRUMENTS

Instructor: Kazumi Tolich Lecture 15

¨ Reading chapter 27.1 to 27.6 ¤ Optical Instruments n Eyes n Cameras n Simple magnifiers n Compound microscopes n Telescopes ¤ Lens aberrations Quiz: 1

¨ If your near point distance is �, how close can you stand to a mirror and still be able to focus on your (beautiful) image? Answer in terms of �, i.e., what is � in ��? Quiz: 15-1 answer

¨ 0.5 �

¨ The near point, �, is the closest point to the eye that the lens is able to focus (~ 25 cm for normal eyes).

¨ If you are a distance 0.5 � in front of a mirror, your image is a distance 0.5 � behind the mirror.

¨ Therefore, you can clearly see your image if the distance from you to your image is �.

¨ The far point is the farthest point at which the eye can focus (∞ for normal eyes). Cameras

¨ The camera lens moves closer to or farther away from the film in order to focus.

¨ The amount of light reaching the film is determined by shutter speed and the �-number:

�-number = = Quiz: 2

¨ A camera’s �-number is reduced from 2.8 to 1.4. Does the light entering the camera (the exposure) increase, decrease, or remains the same, assuming the shutter speed is unchanged? A. Increase B. Decrease C. Remains the same Quiz: 15-2 answer

¨ Increase ¨ �-number = = ¨ Decreasing the �-number will increase the diameter. ¨ This will increase the area through which light enters and thus increases the exposure. Quiz: 3

¨ In the famous novel Lord of the Flies, one of the boys is nearsighted, and his glasses are used to start a fire. Is this a feasible story? A. Yes B. No Quiz: 15-3 answer/Corrective lenses

¨ No

¨ Concave (diverging) lenses would have not been able to focus the rays of the sun.

¨ Nearsightedness is corrected with a diverging lens.

¨ Farsightedness is corrected with a converging lens.

¨ The strength of corrective lenses is usually quoted as refractive power.

1 refractive power = � Example: 1

¨ A nearsighted person cannot focus clearly on objects that are more distant than 2.25 m from her eye. What refractive power lenses are required for her to see distant objects clearly? Apparent size

¨ The apparent size of an object is determined by the actual size of the image on the retina. Magnifying glass

¨ The angular magnifications of a magnifying glass (� < �) are by

� = = (image at infinity) � = = 1 + (image at near point) Example: 2

¨ In your botany class, you examine a leaf using a convex 12-D lens as a simple magnifier. What is the angular magnification of the leaf if the image formed by the lens is at infinity? Assume your near point distance is � = 25 cm. Compound microscope/Demo: 1

¨ The object is placed just outside of the focal length of the objective.

¨ The objective forms a real, enlarged, and inverted image of the object.

¨ The image formed by the objective falls at the focal length of the eyepiece.

¨ The total magnification is the product of the magnification of each lens:

�� = �� = − �� Quiz: 4

¨ A compound microscope has an objective lens with a focal length of 2.2 cm and an eyepiece with a focal length of 5.4 cm. If the image produced by the objective is 12 cm from the objective, what magnification does this microscope produce for a normal eye with its near point of 25 cm? Quiz: 15-4 answer

¨ -25

¨ � = − = − = −25 . . Refracting telescopes

¨ Refractive telescopes work by creating a real, inverted, and diminished image of an object that is much closer than the object.

¨ An eyepiece at its focal length away from the image is used as a simple magnifier to view that image.

¨ The total angular magnification of the telescope is

� = = Quiz: 5

¨ Two telescopes have identical eyepieces, but telescope A is twice as long as telescope B. Compare the total angular magnifications of the telescopes. Quiz: 15-5 answer

¨ �, < �, ¨ The objective lens and the eyepiece must be separated by the sum of the focal lengths, � + �. ¨ Since the scopes have identical eyepieces, telescope A must have a greater �. ¨ � = Example: 3

¨ An astronomical telescope has a total angular magnification of 7.0. The two lenses are 32 cm apart. Find the focal length of each lens. Demo 3

¨ Galilean Telescope: Eyepiece is a diverging lens placed before the focal point of the objective lens. The resulting magnified image is upright.

¨ Keplerian Telescope: Eyepiece is a converging lens placed after the focal point of the objective lens. The resulting magnified image is inverted.

¨ Reflecting Telescope Lens aberration

¨ Spherical aberration occurs when light striking the lens far from the axis does not focus properly. It can be fixed by grinding the lens to a non- spherical shape.

¨ Chromatic aberration occurs when different colors of light focus at different points.

¨ Chromatic aberration can be improved by combining two or more lenses that tend to cancel each other’s aberrations. This only works perfectly for a single wavelength, however.