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Geometric optics

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Reference: Physics for every day phenomena, McGraw-hill.

YOU NEED A RULER !!!

AND A SHARP PENCIL and COLOR PENCILS

TRY WITHOUT HINTS

LENSES— FORMATION OF IMAGES

 

1) Suppose you take 2 prisms one on top the other. See figure.

Can you trace the paths of parallel rays ?

Hint: If you do the things right, all the rays converge to one single point located on the X-axis. This point is called the principal focus f.

Read:

 

This optical system is called a convex lens or converging lens. Convex lenses are thicker in the middle and thinner at the edge such as parallel rays of light are refracted through the principal  focus (f) of the lens. A magnifying glass is a convex lens. It can converge all the rays from the Sun (arriving parallel to the surface because very very far) to a single point. Because you are focusing all the energy to a single point, you can burn a piece of paper.

2) Now position the prisms as shown in the figure. Find the path of the incident and parallel rays of light.

Hint: The rays should be diverged by the lens and should seem to come from a single point (principal focus f)  placed on the left part of the lens.

Read:

This optical system is called a concave lens or diverging lens. Parallel rays of light are diverged so that they appear to come from the principal focus (f) of a concave lens. A concave lens is thinner is the center and thicker at the edge. Objects always look smaller through a concave lens. Applet to understand

DISPERSION OF WHITE LIGHT INTO A SPECTRUM

 

1) Refraction can also explain rainbows. Thee white light is composed of all the colors of a rainbow. They are mixed together and the resulting color is white. All the colors have the same speed in a vacuum or in air. But in a medium like glass, the speed depends of the color that is on the wavelength. Red will slow down less in a glass than blue. So the index of refraction for red is less than for blue. That is red is less refracted than blue.  A) Get a blue and red pencils and complete the figure. Show what happens when white light strikes a prism.

A drop of water, in clouds, acts like a prism. Refraction explains rainbows. Click here.

 

2) A diamond’s index of refraction for red light (656nm) is 2.410. while for blue light (434nm), is 2.450. Suppose white light is incident on the diamond at 30 degrees. Find the angle of refraction for these 2 colors.

Hint: red = n1 = 1, n2= 2.410, angle1 = 30, angle2 = ?

 

3) The index of refraction of crown glass is 1.53 for violet light and it is 1.51 for red.

A) Which color will bend more ?

B) What is the speed of violet light in crown glass?

Hint: V = c/n and c = 300,000km/s

C) What is the speed of red light in crown glass ?

 

3) extra credits (easy)

How much dispersion is there when light goes through a slab of glass ?

n=1.7708 for blue light and n=1.7273. White light in air (n=1) is incident at exactly 45 degrees. Find th angle of refraction for the two colors, then find the difference in those angle in degrees. You should use five significant digits in all calculations.

 

4) advanced

Find the critical angle for ice (n=1.31). In a very cold world, would fiber-optic cables made of ice be better or worse that those made of glass ?

3) A) observe the figure below to understand the formation of an image through a converging lens. You only need 2 rays to find , geometrically, the position of the image and its size. Ray 1 (red)  is parallel to the x-axis so it has to converge to the principal focus F. Ray 2 (blue) goes through the center of the lens and is not bent. The intersection give you the image. Then you can trace other rays (orange).  Note that the lens is symmetric. The x-axis is called the principal axis. The lens has 2 principal focus F. The distance between the center of the lens O and F is called the focal distance f. The focal distance of a lens depends on its size (thicker, more converging) and its material. (index of refraction).

B) It was Newton who showed that white light can be dispersed into a spectrum of colors and that the white light can be reconstituted by sending the dispersed light through a second prism. Can you complete the following figure? Can you find when Newton made this discovery ? Hint: need yellow, green, blue rays + white (make it grey)
Text Box: White Text Box: spectrumText Box: White

B) In the example above, the object was placed between F and 2F. OF is the focal distance f. You get an image inverted, real (can be seen on a screen) and magnified (greater than the object). Now place the object at a distance greater than 2F. Complete the figure below: trace the 2 rays (the one parallel and the one going through 0) to find the location and the size of the imge. Use ruler, mechanical pencil and color pencils. Is the image real ? Inverted ? Smaller ? Greater?

C) advanced. Now place the object between 0 and F. Is the image inverted ? Real? Greater? Smaller  ? (if the rays don’t get to the image, the image is virtual). Extend the rays from both sides to find the image. When you use a magnifying glass, you place the object very close to the lens. The image is larger, erect but virtual.

D) You can also get images using diverging lenses. (concave lenses). Observe the figure below that shows how to find the location and the size of an image using a diverging lens. Then complete the sentences below.