Light Rays and Optics

Solve the following problems in the space provided. Show your work. Write equations in symbolic form before making numerical substitutions, and include the correct units with any numerical result.

1. Light of 520 nm wavelength is used in a double-slit (Young’s) experiment (slit separation 0.45 m). Adjacent dark fringes separated by 2.10 mm are observed on a screen. Determine the slit-to-screen distance.

2. The image of a tree just covers the length of a 5.0-cm plane mirror when the mirror is held vertically 30.0 cm from the eye. The tree is 100 m from the mirror. What is its height?

3. Two thin lenses, the one on the left of focal length -0.200 m and the second of focal length of +0.200 m, are separated by 0.200 m. An object is 0.200 m to the left of the lens. Find the location of the final image both by a ray diagram and by a calculation using the thin-lens equation.

4. An object is located 10.0 cm from the center of a spherical silvered ball 5.0 cm in radius.

(a) Calculate the position of the image.
(b) What is the lateral magnification?
(c) Make a graphical solution.

5. You are given a diffraction grating having an unknown number of lines (rulings) per meter. Using the green line of mercury (546 x 10^-9 m), you find that the angle between the central and the first principal (most in¬tense) maxima is 30° How many lines/meter does the grating have?

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