91Ó°ÊÓ

A narrow beam of white light is incident on a sheet of quartz. The beam disperses in the quartz, with red light $(l≈400nm)$traveling at an angle of $26.3°$with respect to the normal and violet light $(l≈400nm)$ traveling at $25.7°$ . The index of refraction of quartz for red light is $1.45$. What is the index of refraction of quartz for violet light?

A hydrogen discharge lamp emits light with two prominent wavelengths: $656nm$(red) and $486nm$(blue). The light enters

a flint-glass prism perpendicular to one face and then refracts

through the hypotenuse back into the air. The angle between

these two faces is $35°$.

a. Use Figure $35.18$to estimate to $Â\pm 0.002$the index of refraction

of flint glass at these two wavelengths.

b. What is the angle (in degrees) between the red and blue light

as it leaves the prism?

In figure $p35.26$, parallel rays from the left are focused to a point at two locations on the optical axis. find the position of each location, giving your answer as a distance left or right of the lens.

The rays leaving the two-component optical system of FIGUREP$35.27$produce two distinct images of the$1.0cm$-tall object. what are the position (relative to the lens), orientation, and height of each image?

A common optical instrument in a laser laboratory is a beam expander. One type of beam expander is shown in FIGURE P $35.29$. The parallel rays of a laser beam of width w1 enter from the left.

a. For what lens spacing d does a parallel laser beam exit from the right?

b. What is the width w2 of the exiting laser beam?

A 2.0-cm-tall object is $20cm$to the left of a lens with a focal length of$10cm$A second lens with a focal length of $15cm$is$30cm$to the right of the first lens.

a. Use ray tracing to find the position and height of the image. Do this accurately using a ruler or paper with a grid, then make measurements on your diagram.

b. Calculate the image position and height. Compare with your ray-tracing answers in part a.

In FIGURE P$35.30$, what are the position, height, and orientation of the final image? Give the position as a distance to the right or left of the lens.

A $1.0cm$-tall object is $110cm$from a screen. A diverging lens with focal length$-20cm$is $20cm$in front of the object. What are the focal length and distance from the screen of a second lens that will produce a well-focused, $2.0cm$-tall image on the screen?

A $15cm$-focal-length converging lens is $20cm$to the right of a $7.0cm$-focal-length converging lens. A $1.0cm$-tall object is distance L to the left of the first lens.

a. For what value of L is the final image of this two-lens system halfway between the two lenses?

b. What are the height and orientation of the final image?

Yang can focus on objects $150cm$ away with a relaxed eye. With full accommodation, she can focus on objects $20cm$away. After her eyesight is corrected for distance vision, what will her near point be while wearing her glasses?