An object is placed to the left of a lens, and a real image is formed to the right of the lens. The image is inverted relative to the object and is one-half the size of the object.

What kind of lens, converging or diverging, is used to produce this image?

A camera is supplied with two interchangeable lenses, whose focal lengths are 35.0 and 150.0 mm. A woman whose height is 1.60 m stands 9.00 m in front of the camera. What is the height (including sign) of her image on the film, as produced by (a) the 35.0-mm lens and (b) the 150.0-mm lens?

The owner of a van installs a rear-window lens that has a focal length of -0.300 m. When the owner looks out through the lens at a person standing directly behind the van, the person appears to be just 0.240 m from the back of the van, and appears to be 0.34 m tall (a) How far from the van is the person actually standing , and (b) how tall is the person?

(a) For a diverging lens (f = -20.0 cm), construct a ray diagram to scale and find the image distance for an object that is 20.0 cm from the lens. (b) Determine the magnification of the lens from the diagram.

If an object is placed at the focal point of a converging lens, the image is (a) at zero, (b) also at the focal point, (c) at a distance equal to twice the focal length, (d) at infinity.

An object is placed 20.0 cm to the left of a diverging lens (f = -8. 00 cm). A concave mirror (f = 12.0 cm) is placed 30.0 cm to the right of the lens. (a) Find the final image distance, measured relative to the mirror. ( b) Is the final image real or virtual? (c) Is the final image upright or inverted with respect to the original object?

You are trying to photograph a bird sitting on a tree branch, but a tall hedge is blocking your view. However, as the drawing shows, a plane mirror reflects light from the bird into your camera. For what distance must you set the focus of the camera lens in order to snap a sharp picture of the bird's image?

$$\begin{array} { l } { \text { Show that an integral domain with the property that every strictly } } \\ { \text { decreasing chain of ideals } I _ { 1 } \supset I _ { 2 } \supset \cdots \text { must be finite in length is } } \\ { \text { a field. } } \end{array}$$

Add. Write the answer in standard form.

$$(2x^{2} - 2x + 6) + (11x^{3} - x^{2} - 2 + 5x)$$

A slide projector has a converging lens whose focal length is 105.00 mm. (a) How far (in meters) from the lens must the screen be located if a slide is placed 108.00 mm from the lens? (b) If the slide measures 24.0 mm x 36.0 mm, what are the dimensions (in mm) of its image?

An object is located 9.0 cm in front of a converging lens (f = 6.0 cm). Using an accurately drawn ray diagram, determine where the image is located.

Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Rhinoviruses typically cause common colds. In a test of the effectiveness of echinacea, 40 of the 45 subjects treated with echinacea developed rhinovirus infections. In a placebo group, 88 of the 103 subjects developed rhinovirus infections (based on data from "An Evaluation of Echinacea Angustifolia in Experimental Rhinovirus Infections ," by Turner et al., New England Journal of Medicine, Vol. 353, No. 4). We want to use a 0.05 significance level to test the claim that echinacea has an effect on rhinovirus infections. Test the claim using a hypothesis test.

A small postage stamp is placed in front of a concave mirror (radius = R), such that the image distance equals the object distance. (a) In terms of R, what is the object distance? (b) What is the magnification of the mirror? (c) State whether the image is upright or inverted relative to the object. Draw a ray diagram to guide your thinking.

A ray of light impinges from air onto a block of ice (n = 1.309) at a

$$60.0 ^ { \circ }$$

angle of incidence. Assuming that this angle remains the same, find the difference

$$\theta _ { 2 , \text { ice } } - \theta _ { 2 , \text { water } }$$

in the angles of refraction when the ice turns to water (n = 1.333).