HardPhysicsHigh School (11–12)OpticsNumericalpython

In a school experiment a student fixes a small bright object on an optical bench and moves a convex…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

In a school experiment a student fixes a small bright object on an optical bench and moves a convex lens to different distances from it. For each distance she moves a screen until the image is sharp, and she reads the distance of the screen from the lens. She records five pairs of readings, each in centimetre. The object distance and the image distance are $25.0$ and $100.4$ , then $30.0$ and $59.6$ , then $40.0$ and $40.5$ , then $50.0$ and $33.1$ , and finally $60.0$ and $30.2$ . Treat the lens as thin and measure all distances from its centre. Find the focal length from the first pair of readings. Find the mean of the five values. Say how far the largest and smallest values differ, as a percentage of the mean. Then plot the reciprocal of the image distance against the reciprocal of the object distance. Find the focal length from the intercept.

Need a reminder? The key ideaShow

For a thin lens, $\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}$ and $m = \dfrac{v}{u}$ , with distances from the optical centre and positive in the direction of the light. A real object has $u < 0$ . The lens maker's formula is $\dfrac{1}{f} = (n-1)\left(\dfrac{1}{R_1} - \dfrac{1}{R_2}\right)$ .

The worked solution

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