Geometrical Optics Lab PDF

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Physics Lab...

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Geometrical Optics - Lenses and Mirrors

Victoria R. Weinsheimer Conducted on 05/11/18 Lab Partners: Graceanne Lopez & Jessie Ertman

PURPOSE  

To investigate basic ideas of geometrical optics. To verify the principle of reversibility of light rays and the magnification relationship using two different focal length convergent lenses.

INTRODUCTION If a ray of light could be observed approaching and reflecting off of a flat mirror, then the behavior of the light as it reflects would follow a predictable law known as the law of reflection. The law of reflection states that the angle of the incident ray is equal to the angle of the reflected ray. Thus,

ϴI = ϴR In contrast, refraction is defined as the changing of a light ray's direction (loosely called bending) when it passes through variations in matter. The law of refraction, also called Snell's Law, states that the incident ray, the refracted ray, and the normal to the interface, all lie in the same plane. Furthermore,

n1sinϴ1 = n2sinϴ2 Additionally, the magnification of a lens is defined as the ratio of the image size to the object size. Therefore, hq / hp = Magnification The source and image location data can also be used to determine the focal length using the Lens Equation: 1/f = 1/p + 1/q

PROCEDURE 1. We chose two different focal length and recorded their values in our data table. 2. We set up the source, the lens and a screen as explained by our lab instructor. 3. We measured the constant height of the source, hp, and recorded it in our table. 4. We obtained the image of the image on the screen and measured its height, hq. 5. We then checked for reversibility by exchanging the positions of the source and the screen with respect to the lens. We verified that a clear image was shown. 6. We repeated steps 3-5 for 5 different distances on the same lens. 7. We then conducted the same last steps using a second lens with a different focal length.

DATA

Focal Length:

Lens #1: 9 cm

Lens #2: 14.3 cm

± .01 cm

Setup #

Source distance

Image distance

Source height hp [cm]

Image height hq [cm]

Magnificatio n hq/hp

1 2 3 4 5

20.0 50.0 38.0 25.0 43.5.0

50.0 20.0 25.0 38.0 23.5.0

2.0 2.0 2.0 2.0 2.0

4.5 1.0 1.4 3.1 1.3

2.25 .5 .7 1.55 .65

Image height hq [cm]

Magnificatio n hq/hp

7.9 0.9 2.2 1.7 1.3

3.95 0.45 1.1 .85 .65

Setup #

Source distance [cm]

Image distance [cm]

Source height hp [cm]

1 2 3 4 5

11.0 57.1 18.6 20.8 78.5

57.1 11.0 20.8 18.6 10.8

2.0 2.0 2.0 2.0 2.0

± .01 cm

± .01 cm

± .01 cm

± .01 cm

PRESENTATION Lens #1 First & Second Setup

Lens #2 First & Second Setup

1/f = 1/p + 1/q 1/f = 1/20 + 1/50 1/f = .07 f = 1/.07 f = 14.29 cm

1/f = 1/p + 1/q 1/f = 1/11 + 1/57.1 1/f = .1084 f = 1/.1084 f = 9.22 cm

Lens #1 Third & Fourth Setup 1/f = 1/p + 1/q 1/f = 1/38 + 1/25 1/f = .0663 f = 1/.0663 f = 15.08 cm

Lens #2 Third & Fourth Setup 1/f = 1/p + 1/q 1/f = 1/18.6 + 1/20.8 1/f = .1018 f = 1/.1018 f = 9.82 cm

Lens #1 Fifth Setup 1/f = 1/p + 1/q 1/f = 1/43.5 + 1/23.5 1/f = .0655 f = 1/.0655 f = 15.26 cm

Lens #2 Fifth Setup 1/f = 1/p + 1/q 1/f = 1/78.5 + 1/10.8 1/f = .1053 f = 1/.1053 f = 9.49 cm

Avg. focal length for lens #1: 14.88 cm

PERCENT DIFFERENCE Lens #1: 14.88 - 14.3 14.3

x 100 = 4.06 %

Lens #2: 9.51 - 9.0 9.0

x 100 = 5.67 %

Avg. focal length for lens #2: 9.51 cm

CONCLUSION As you can see me and my lab partners indeed verified the magnification relationship between image distance and source distance. We clearly verified the relationship because there only resulted a less than 6% difference between measured and expected focal lengths using the formula: 1/f = 1/p + 1/q, where f is focal length, q is image distance and p is source distance. It is important to note that this 6% difference came from measurement uncertainties using a metric ruler. In addition, me and my lab partners verified the principle of reversibility clearly when a sharp image appeared when we exchanged the positions of the source and the screen with respect to the lens. To conclude, the experiment was done well but at a slow pace. We were not able to get up to parts B, C, and D in the lab manual....