# Reflection and Mirrors Review

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### Part C: Calculations and Explanations

33. Distinguish between diffuse and regular (specular) reflection in terms of both cause and result.

 Answer: Specular (or regular) reflection occurs when light reflects off a microscopically smooth surface. Light rays which are incident within a beam will reflect and remain in the beam. Diffuse reflection occurs when light reflects off a microscopically rough surface. Light rays which are incident in a beam will diffuse (or scatter) and reflect in a variety of directions. In each case the law of reflection holds; in diffuse reflection, the normals for each individual ray are not oriented in the same direction.

Specular vs. Diffuse Reflection

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34. Write the formulae which show the relationship between image distance, object distance and focal length, and the magnification of an object/image.

 Answer: Please know this one: where s and h stand for object distance and object height, and s' and h' stand for image distance and image height, and f stands for focal length, and M stands for magnification.

The Mirror Equation - Concave Mirrors

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35. Fill in the blanks below for the problem-solving rules:

Focal lengths, object and image distances are ________ if they are on the reflective side of the mirror. Object and image heights are positive if they are ________ the principle axis.

 Answer: Focal lengths, object and image distances are positive if they are on the reflective side of the mirror. Object and image heights are positive if they are below the principle axis. The do and di values (s and s') and the ho and hi values (h and h') can have positive and negative values associated with them. In physics, a + or - in front of a quantity is always descriptive of some physical feature. In ray optics, a + distance (do, di or f) means in front of the mirror as the object; a negative distance means behind the mirror. A + height means above the principal axis and a - height means below the principal axis.

The Mirror Equation - Concave Mirrors (6 seconds)

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36. What is the focal length of a mirror which gives an image 3 meters away when an object is placed 150 cm from it?

 Answer: 100 cm or 1.0 m Use the mirror equation: 1/di + 1/do = 1/f where di = +300 cm and do = +150 cm. (Note: since di > do, it must be a concave mirror and the image must be real.) Substitute and solve for f. 1/(150 cm) + 1/(300 cm) = 1/f 1/f = 3/(300 cm) or 0.01/cm f = 100 cm = 1.0 m

The Mirror Equation - Concave Mirrors

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37. Where is the image located when an object is placed 60 cm from a mirror which has a focal length of 20 cm?

 Answer: 30 cm Use the mirror equation: 1/di + 1/do = 1/f where d0 = +60 cm and f = +20 cm. Substitute and solve for di. 1/(60 cm) + 1/di = 1/(20 cm) 1/di = 1/(20 cm) - 1/(60 cm) = 2/(60 cm) di = 30 cm

The Mirror Equation - Concave Mirrors

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38. How far would an object need to be placed from a mirror of focal length 10 cm if it is to produce an image which is 20 cm BEHIND the mirror?

 Answer: 6.67 cm Use the mirror equation: 1/di + 1/do = 1/f where di = -20 cm and f = +10 cm. Substitute and solve for do. 1/do + 1/(-20 cm) = 1/(10 cm) 1/do = 1/(10 cm) - 1/(-20 cm) = 3/(20 cm) = 0.15/cm do = 6.67 cm

The Mirror Equation - Concave Mirrors

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39. A mirror with a focal length of -100 cm is used to form an image. An object is placed 50 cm in front of the mirror.

a. Where is the image located?

b. What type of mirror is being used in this problem?

 Answer: -33.3 cm; convex mirror Use the mirror equation: 1/di + 1/do = 1/f where d0 = +50 cm and f = -100 cm. (Note: this is a convex mirror since the focal length is negative.) Substitute and solve for di. 1/(50 cm) + 1/di = 1/(-100 cm) 1/di = 1/(-100 cm) - 1/(50 cm) = -3/(100 cm) or -0.03/cm di = -33.3 cm

The Mirror Equation - Convex Mirrors

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40. An object is placed 20 cm from a mirror of focal length 10 cm. The object is 5 cm tall. Where is the image located? How tall is the image?

 Answer: di = 20 cm; hi = -5 cm Use the mirror equation: 1/di + 1/do = 1/f where d0 = +20 cm and f = 10 cm. Substitute and solve for di. 1/(20 cm) + 1/di = 1/(10 cm) 1/di = 1/(10 cm) - 1/(20 cm) = 1/(20 cm) or 0.05/cm di = 20 cm Use the magnification ratio to solve for hi: hi/ho = -di/do where ho = 5 cm. hi /(5 cm) = - (20 cm)/(20 cm) hi = - [(20 cm)/(20 cm)]•(5 cm) hi = -5 cm

The Mirror Equation - Concave Mirrors

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41. A 20 cm tall object produces a 40 cm tall real image when placed in front of a curved mirror with a focal length of 50 cm. Determine the place that the object must be located to produce this image.

 Answer: 75 cm Given: ho = 20 cm, hi = -40 cm, f = 50 cm (Note: hi is negative since the image is real.) Strategy: use the object and image height values with the magnification ratio in order to generate an expression for di in terms of do. Then substitute the expression into the mirror equation to solve for the object distance. hi/ho = -di/do (-40 cm)/(20 cm) = -di/do -2 = = -di/do di = 2•do Now substitute this expression into the mirror equation. 1/do+ 1/(2do) = 1/(50 cm) 2/(2do) + 1/(2do) = 1/(50 cm) 3/(2do) = 1/(50 cm) 2do= 150 cm do = 75 cm

The Mirror Equation - Concave Mirrors

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42. A mirror is used to produce a virtual image that is 5 times bigger than the object. If the focal length of the mirror is 100 cm, where will the image be located?

 Answer: -400 cm Given: M = +5 , f = 100 cm (Note: M is positive since the image is virtual.) Strategy: use the magnification value with the magnification ratio in order to generate an expression for do in terms of di. Then substitute the expression into the mirror equation to solve for the object distance. M = hi/ho = -di/do +5 = -di/do do = = -di/5 Now substitute this expression into the mirror equation. 1/(-di/5)+ 1/(di) = 1/(100 cm) -5/(di) + 1/(di) = 1/(100 cm) -4/(di) = 1/(100 cm) di = -400 cm

The Mirror Equation - Concave Mirrors

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