2.8 Microscopes and telescopes  (Page 9/16)

A point source of light is 50 cm in front of a converging lens of focal length 30 cm. A concave mirror with a focal length of 20 cm is placed 25 cm behind the lens. Where does the final image form, and what are its orientation and magnification?

Copy and trace to find how a horizontal ray from S comes out after the lens. Use $n_{\text{glass}}=1.5$ for the prism material.

Copy and trace how a horizontal ray from S comes out after the lens. Use $n=1.55$ for the glass.

Copy and draw rays to figure out the final image.

By ray tracing or by calculation, find the place inside the glass where rays from S converge as a result of refraction through the lens and the convex air-glass interface. Use a ruler to estimate the radius of curvature.

A diverging lens has a focal length of 20 cm. What is the power of the lens in diopters?

Two lenses of focal lengths of $f_1$ and $f_2$ are glued together with transparent material of negligible thickness. Show that the total power of the two lenses simply add.

What will be the angular magnification of a convex lens with the focal length 2.5 cm?

What will be the formula for the angular magnification of a convex lens of focal length f if the eye is very close to the lens and the near point is located a distance D from the eye?

Use a ruler and a protractor to draw rays to find images in the following cases.

(a) A point object located on the axis of a concave mirror located at a point within the focal length from the vertex.
(b) A point object located on the axis of a concave mirror located at a point farther than the focal length from the vertex.
(c) A point object located on the axis of a convex mirror located at a point within the focal length from the vertex.
(d) A point object located on the axis of a convex mirror located at a point farther than the focal length from the vertex.
(e) Repeat (a)–(d) for a point object off the axis.

Where should a 3 cm tall object be placed in front of a concave mirror of radius 20 cm so that its image is real and 2 cm tall?

A 3 cm tall object is placed 5 cm in front of a convex mirror of radius of curvature 20 cm. Where is the image formed? How tall is the image? What is the orientation of the image?

You are looking for a mirror so that you can see a four-fold magnified virtual image of an object when the object is placed 5 cm from the vertex of the mirror. What kind of mirror you will need? What should be the radius of curvature of the mirror?

Derive the following equation for a convex mirror:

$\frac{1}{VO}-\frac{1}{VI}=\text{−}\frac{1}{VF}$ ,

where VO is the distance to the object O from vertex V , VI the distance to the image I from V , and VF is the distance to the focal point F from V . ( Hint : use two sets of similar triangles.)

(a) Draw rays to form the image of a vertical object on the optical axis and farther than the focal point from a converging lens. (b) Use plane geometry in your figure and prove that the magnification m is given by $m=\frac{h_{\text{i}}}{h_{\text{o}}}=\text{−}\frac{d_{\text{i}}}{d_{\text{o}}}.$