Homework Set 5: Due Wednesday, March, 17 From Chapter 5: P2, P8, P10, P11, From Chapter 6: P1, P2, P6, PM2,

Single-Lens Instruments Eyeglasses: Spherical Corrections Eyeglasses: Cylindrical Corrections Contact Lenses Magnifying Glass

Eyeglasses: Spherical Corrections Normal focus: –Ciliary muscles relax: see light ray from infinity. This is the far point of the vision. –Muscles tense: shorten the focal length, see object clearly about 25cm away. This is the near point of the vision.

We can think of the eye as effectively consisting of two lenses: –First is used when see infinity (power ~ 60 D). Lens I

–Second is used when see 25cm. One needs an additional 1/f=1/0.25=4 D lens to convert rays from 25cm away object into parallel rays. The total focusing power is now ~ 64 D. Lens I Lens II Thus, during accommodation, the change of power is from 60D to 64 D.

When a relaxed eye has too much focusing power, the image is in front of the retina (myopia). It cannot see parallel rays from infinity. However, it can see things close by

For example, if when relaxed, an eye has focusing power of 61D, it is effectively made of two lenses with focusing power of 60D and 1D. The first one is what is needed to see objects far away, and the second one has a focal length of 1m. If an object is just one meter away, the second lens converts its light-rays into parallel rays. Thus 1m is the far point that this eye can see!

If the far point is at 100 cm, then one needs a diverging lens to convert the light ray from infinity to a light ray from 100 cm away. The focal length of the lens then must be – 100cm. The power of the lens is –1 = – 1D correction.

When a relaxed eye has too little power (less than 60 D, say 58 D), then it has maximum focusing power of 62D. When focusing on an object 25cm away, the image is behind the retina (hyperopia).

When at 62D, it can be viewed as two lenses 60D+2D. Thus it can only see things clearly at ½ m =50 cm away. We say the near point is 50cm. Need a prescription of +2D (converging lens) to correct.

When aged, the eye does not accommodate well (does not have a full range of 4D). For example, one might has a focusing range (61D-63D). Then one has the so-called presbyopia, a bifocal correction is needed.

A summary Normal vision See infinity See 25cm away Myopia Hypropia Presbyopia Focusing power

Astigmatism is a vision condition that occurs when the front surface of your eye, the cornea, is slightly irregular in shape. – curved in one direction but not the other. Or the extent of curving is different in different directions. This irregular shape prevents light from focusing properly on the back of your eye, the retina. –the focal length of the astigmatic eye is different for rays on one plane than for those in a perpendicular plane.

As a result, your vision may be blurred at all distances. People with severe astigmatism will usually have blurred or distorted vision, while those with mild astigmatism may experience headaches, eye strain, fatigue or blurred vision at certain distances. Almost all levels of astigmatism can be optically corrected with properly prescribed and fitted eyeglasses and/or contact lenses. –Cylindrical lens: curved in one direction but not the other. Or the extent of curving is different in different directions. Corneal modification is also a treatment option for some patients.

Contact Lens Since the contact lenses are worn in contact with the cornea, the image has the same size as if the lenses are absent. (This is not the case with the normal glasses.) Very easy for correcting astigmatism because the front surface of the contact lenses are always spherical.

Magnifying glass A converging lens with a focusing power. Can be used to convert rays from its focal point into parallel rays, and then can be viewed with a relaxed eye. Lens I Lens II

How to use a Magnifying Glass A wrong way to held a magnifying glass: holding it at arm’s length. –The image does look bigger than the object, but not the biggest. The correct way is to held it next to your eye and place the object at the focal point of the magnifying glass. –So there no magnification, but the image is the BIGGEST! The same principle is used for close- up photography.

Magnifying power The magnifying power is the ratio between the sizes of the images when the object is f-cm away and when it is 25-cm away. Magnification = 25/f (cm) If f=10cm, the magnifying lens has magnifying power of 2.5. One can get as a large image as possible using a magnifying glass with very short focal length.