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# The thin lens equation relates the object and image distances to the focal length of the lens.

The thin lens equation relates the object and image distances to the focal length of the lens. If the object distance can be made very large ( = 0) then the equation reduces to the image, which will be very small, being at the focal length of the lens.

Place the white viewing screen at the far end of the magnetic optical rail. Place the cross arrow on the light source at the other end of the rail.

Place the 75 mm (0.075m) convex lens on a magnetic holder at the far end of the magnetic optical rail near the screen (see figure 7.4). The lens should be centered on the opening in the holder.

Adjust the lens until a sharp very small image is formed. Since the object i.e. the cross arrow target is far away, the distance between the lens and the screen is approximately the focal length of the lens. Record the focal length of the lens and object distance.

Focal length of lens

Object distance

Explain why this approximate focal length method works using the thin lens equations.

Parallel light rays should impinge on the circular side of the cylindrical 'lens'. Using a small white card, look for the 'focus' of the lens. As you move the card back and forth, you should see the rays converge into a single line. (Ignore the rays above the cylindrical lens which do not change the spacing.) Using a ruler, measure the 'focal length' (distance from the 'lens' to the focal point) of this one dimensional lens. Record the value below.

Approximate focal length of cylindrical 'lens'

If you reverse the cylindrical lens so the flat side is facing the light

Figure 7.4: Arrangement of components for the approximate focal length measurement for a single lens

side to locate the position of the component on the rail side scale (see figure 7.3. Each component should be centered on the holder.

Attach the cross arrow target (CAT) to the front of the light source. Place the the light source at one end of the rail. Place the 75 mm (0.075m) convex lens on a holder and position it 30 cm (.3 m) from the CAT. See Figure 7.5

Calculate the location of the image formed by the lens using the thin lens equation. Calculate the size and orientation of the image using the magnification equation. Show your calculations below

Place the view screen on a holder and place it at the calculated image position. Make small changes to the screen position to get a good focus.

Record the measured object and image distance below.

Object distance

Image distance

Using the thin lens equation and the measured object and image distances, calculate the (measured) focal length of the lens.

Does the measured focal length agree with the value shown on the lens (75 mm)? Calculate the percentage error between the measured focal length and the value shown on the lens.

Percentage error

Measure and record below the image size and orientation. (The circle on the CAT is 1 cm in diameter.)

Image size

Figure 7.5: Arrangement of components for the focal length measurement for a single lens

Image orientation

In the thin lens equation, the sum of the inverses of the object distance and image distance are equal to the inverse of the focal length. If the image and object distance are interchanged, another image should be observed on the screen assuming the total distance between object and image is not changed. Move the lens so the distance between the CAT and the lens is the calculated image distance (di). Is a sharp image formed by interchanging the object and image distance? What happens to the magnification? Explain

7.3.4     Questions

1.   Explain how a lens uses refraction to bend light. Why is one or both of the surfacesof the lens 'spherical'

2.1.   Explain what the terms focal length and focal point mean.

2.   In the 'Procedure for Approximate Focal Length' the light rays were not at an infinitedistance and thus not parallel to the principle axis. Use the thin lens equation to estimate how accurate you expect this type of measurement to be.

3.   A beacon in a lighthouse is designed to project a beam of parallel light rays. Thebeacon consists of a small intense light bulb and a large converging lens. Should the light bulb be place at a distance greater than the focal length of the lens, at the focal point of the lens or a distance less than the focal length of the lens?

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