33. Geometric Optics

You want to produce a mirror that can produce an upright image that would be twice as tall as the object when placed 5 cm in front of it. What shape should this mirror be? What radius of curvature should the mirror have?

(II) A small candle is 41 cm from a concave mirror having a radius of curvature of 24 cm.

(a) What is the focal length of the mirror?

(b) Where will the image of the candle be located?

(c) Will the image be upright or inverted?

(I) A solar cooker, really a concave mirror pointed at the Sun, focuses the Sun’s rays 17.2 cm in front of the mirror. What is the radius of the spherical surface from which the mirror was made?

Each student in a physics lab is assigned to find the location where a bright object may be placed in order that a concave mirror, with radius of curvature r = 54cm, will produce an image three times the size of the object. Two students complete the assignment at different times using identical equipment, but when they compare notes later, they discover that their answers for the object distance are not the same. Explain why they do not necessarily need to repeat the lab, and justify your response with a calculation.

You look at yourself in a shiny 8.4-cm-diameter Christmas tree ball. If your face is 25.0 cm away from the ball’s front surface, where is your image? Is it real or virtual? Is it upright or inverted?

A shaving or makeup mirror is designed to magnify your face by a factor of 1.8 (when compared to a flat mirror) when your face is placed 20.0 cm in front of it.

(a) What type of mirror is it?

(b) Describe the type of image that it makes of your face.

(c) Calculate the required radius of curvature for the mirror.

A 2.0-cm-tall object is placed in front of a mirror. A 1.0-cm-tall upright image is formed behind the mirror, 150 cm from the object. What is the focal length of the mirror?

A spherical, concave shaving mirror has a radius of curvature of 32.0 cm. Where is the image? Is the image real or virtual?

BIO A keratometer is an optical device used to measure the radius of curvature of the eye's cornea—its entrance surface. This measurement is especially important when fitting contact lenses, which must match the cornea's curvature. Most light incident on the eye is transmitted into the eye, but some light reflects from the cornea, which, due to its curvature, acts like a convex mirror. The keratometer places a small, illuminated ring of known diameter 7.5 cm in front of the eye. The optometrist, using an eyepiece, looks through the center of this ring and sees a small virtual image of the ring that appears to be behind the cornea. The optometrist uses a scale inside the eyepiece to measure the diameter of the image and calculate its magnification. Suppose the optometrist finds that the magnification for one patient is 0.049. What is the absolute value of the radius of curvature of her cornea?

Let the focal length of a convex mirror be written as ƒ = ―|ƒ|. Show that the lateral magnification m of an object a distance dₒ from this mirror is given by m = |ƒ| / (dₒ +|ƒ| ). Based on this relation, explain why your nose looks bigger than the rest of your face when looking into a convex mirror.