33. Geometric Optics

A 4 cm tall object is placed in 15 cm front of a concave mirror with a focal length of 5 cm. Where is the image produced? Is this image real or virtual? Is it upright or inverted? What is the height of the image?

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?

A 4 cm tall object is placed 15 cm in front of a concave mirror with a focal length of 5 cm. Where is the image produced? Is this image real or virtual? Is it upright or inverted? What is the height of the image?

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?

(I) How far from a concave mirror (radius 30.0 cm) must an object be placed if its image is to be at infinity?

(II) The lateral magnification of a convex mirror is +0.75 for objects 3.2 m from the mirror. What is the focal length of this mirror?

(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?

(II) 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?

(II) A dentist wants a small mirror that, when 2.00 cm from a tooth, will produce a 3.0 x upright image. What kind of mirror must be used and what must its radius of curvature be?

(II) The image of a distant tree is virtual, very small, and 13.0 cm behind a curved mirror. What kind of mirror is it, and what is its radius of curvature?

(II) A 4.2-cm-tall object is placed 26 cm in front of a spherical mirror. It is desired to produce a virtual image that is upright and 3.2 cm tall.

(a) What type of mirror should be used?

(b) Where is the image located?

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

(d) What is the radius of curvature of the mirror?

(II) (a) Where should an object be placed in front of a concave mirror so that it produces an image at the same location as the object? (b) Is the image real or virtual? (c) Is the image inverted or upright? (d) What is the lateral magnification of the image?

(II) When walking toward a concave mirror you notice that your image flips at a distance of 0.80 m from the mirror. What is the radius of curvature of the mirror? [Hint: Carefully examine Section 32–4.]

An object is placed 21 cm from a certain mirror. The image is half the height of the object, inverted, and real. How far is the image from the mirror, and what is the radius of curvature of the mirror?

(II) In Example 32–4, show that if the object is moved 10.0 cm farther from the concave mirror, the object’s image size will equal the object’s actual size. Stated as a multiple of the focal length, what is the object distance for this “actual-sized image” situation?

(II) 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.

(II) 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 1.80-m-tall person stands 4.20 m from a convex mirror and notices that he looks precisely half as tall as he does in a plane mirror placed at the same distance. What is the radius of curvature of the convex mirror? (Assume that θ ≈ θ .) [Hint: The viewing angle is half.]

(II) An object 4.0 mm high is placed 18 cm from a convex mirror of radius of curvature 18 cm.

(b) Show that the (negative) image distance can be computed from Eq. 32–2 using a focal length of -9.0cm.

(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?

(II) A spherical mirror of focal length ƒ produces an image of an object with lateral magnification m. (a) Show that the object is a distance dₒ = ƒ (1 - (1/m)) from the reflecting side of the mirror. (b) Use the relation in part (a) to show that, no matter where an object is placed in front of a convex mirror, its image will have a lateral magnification in the range 0 ≤ m ≤ + 1 .

(III) An object is placed a distance r in front of a wall, where r exactly equals the radius of curvature of a certain concave mirror. At what distance from the wall should this mirror be placed so that a real image of the object is formed on the wall? What is the lateral magnification of the image?

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.