ChemPhys 173/273

Unit 1: Reflection and Mirrors

Problem Set A

 

Overview:

Problem Set A targets your ability to use the mirror equation in order to solve relatively simple word problems involving the location and size of images formed by concave and convex mirrors. There are twenty 1-step and 2-step problems which require the use of the two equations and a few conceptual understandings. The two equations - the mirror equation and the magnification ratio - are shown below:

Mirror Equation

1 / f = 1/ do + 1 / di

Magnification Ratio

M = hi / ho = - di / do

In the above equations, the variable do represents the object distance or the distance between the mirror surface and the object. The variable di represents the image distance or the distance between the mirror surface and the image. The variable ho represents the object height and the variable hi represents the image height. The variable f stands for the focal length of the mirror. The variable M stands for the magnification of the image; it represents how many times bigger the image is than the object. In some problems, the focal length is not stated; rather, the radius of curvature of the spherical mirror is stated. The radius of curvature (R) is simply twice the focal length value (R = 2•f).

In Set A, the above equations are used to assist in the solution of physics word problems. Values of two or more quantities are typically expressed in the problem; and the goal of the word problem is to solve for an unknown quantity. Substitutions of known quantities will have to be made into the above equations and proper algebraic manipulations must be performed in order to solve for the unknown quantity.

 

Developing Effective Problem-Solving Habits

Effective problem-solving habits should be practiced in the solution of these problems. Establishing good habits early in the course will serve a student as more difficult problems appear in later sets and later units. Such habits include the following:

  1. Read the problem carefully and develop a mental picture of the physical situation. Diagram the situation if necessary.
  2. Identify the known and unknown quantities in an organized manner. Equate given values to the symbols used to represent the corresponding quantity (e.g., f = 21.2 cm).
  3. Plot a strategy for solving for the unknown quantity.
  4. Identify the appropriate formula(s) to use.
  5. Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.

 

Sign Conventions

Perhaps one of the most problematic areas of the two Unit 1 problem sets is dealing with the sign conventions associated with the image distance, focal length and image height. The table below summarizes the sign conventions associated with these quantities.

Quantity

Sign Convention

do

For our purposes, the object distance (do) will always be positive.

ho

For our purposes, the object height (ho) will always be positive.

di

A positive image distance (di) corresponds to an image location on the same side of the mirror as the object. A negative image distance (di) corresponds to an image located behind the mirror.

hi

A positive image height (hi) corresponds to an upright image. A negative image height (hi) corresponds to an inverted image. Since all upright images (positive hi values) are virtual images located behind the mirror; upright images will thus be virtual images with negative image distances. Likewise, inverted images with their negative hi values are real images that have positive image distance values.

f

A concave mirror will have a positive focal length (f) and a convex mirror will have a negative focal length (f).

M

Magnification values are positive whenever image heights (hi) are positive. Thus, positive M values correspond to upright, virtual images located behind the mirror surface. And negative M values correspond to inverted, real images located on the object's side of the mirror.

When reading a problem, give attention to cues within the problem in order to determine the sign on the given quantity. For instance, in problems #11, #13 and #15, the distance from the focal point to a mirror is stated. This is simply a distance value corresponding to the absolute value of the focal length. Whether the focal length is positive or negative is dependent upon whether the mirror is concave or convex. A careful reading of the problem and an understanding of the sign convention on focal length (as stated in the table above) allows one to make the decision about the sign on f. As a second example, problems #17, #18 and #20 describe an image being located a stated distance from a curved mirror. The stated value is simply the absolute value of the image distance. Whether the di value is positive or negative depends upon whether the image is in front of or behind the mirror. A careful reading of the problem statement along with an understanding of the sign convention for image distance (as stated in the table above) allows one to make the decision about the sign on di. These types of decisions are critical to your success on the Unit 1 problems. Making the correct decisions have nothing to do with your mathematical skills; rather, they are tests of your conceptual understandings and your willingness to read a problem carefully and to give attention to details which may be important.

 

Additional Readings/Study Aids:

The following pages from The Physics Classroom tutorial may serve to be useful in assisting you in the proper use of the mirror equation and magnification ratio and in your ability to make the connection between the image characteristics and the proper sign (+ vs. -) for stated values.

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View Sample Problem Set.

 

Problem

Description

Audio Link
1

Routine calculation of di.

2

Referring to the previous problem; routine calculation of M.

3

Routine calculation of di.

4

Routine calculation of di.

5

Referring to the previous problem; routine calculation of M.

6

Routine calculation of di.

7

Referring to the previous problem; routine calculation of M.

8

Calculation of di. Requires two steps with the first step being the determination of the focal length.

9

Calculation of di. Requires two steps with the first step being the determination of the focal length.

10

Referring to the previous problem; routine calculation of M.

11

Routine calculation of di; requires conceptual decision-making with regards to sign conventions.

12

Referring to the previous problem; routine calculation of M.

13

Routine calculation of di; requires conceptual decision-making with regards to sign conventions.

14

Referring to the previous problem; routine calculation of M.

15

Routine calculation of di; requires conceptual decision-making with regards to sign conventions.

16

Referring to the previous problem; routine calculation of M.

17

Routine calculation of f; requires conceptual decision-making with regards to sign conventions.

18

A multistep problem which combines algebraic problem solving with an understanding of the f-R relationship and the ability to make conceptual decisions with regards to sign conventions.

19

Referring to the previous problem; routine calculation of M.

20

Routine calculation of do; requires conceptual decision-making with regards to sign conventions.

 

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