Magnification Calculations

3.6 Magnification Calculations

How to Calculate Magnification

• To calculate magnification, you need:

  • Distances:

  • Distance of the object

  • Distance of the image

  • Heights:

  • Height of the object

  • Height of the image

Predicting Actual Height of an Image in a Concave Mirror

• Principal concepts include:

  • C: Center of curvature

  • F: Focal point

  • Principal Axis: The line that runs through the center of the mirror

Magnification Formula for Heights

• Use the formula:

  • M = \frac{hi}{ho}

  • Where:

    • M = Magnification

    • h_i = Height of the image

    • h_o = Height of the object

• Rearranged forms include:

  • hi = ho \times M

  • ho = \frac{hi}{M}

Magnification Formula for Distances

• Use the formula:

  • M = \frac{di}{do}

  • Where:

    • d_i = Image distance

    • d_o = Object distance

• Rearranged forms include:

  • di = do \times M

  • do = \frac{di}{M}

Simplified Magnification Formula

• Expressed as:

  • M = \frac{Image}{Object}

Things to Remember

• Units must be the same to calculate magnification.

• Larger images will have a magnification greater than one (

  • M > 1 ).

• Smaller images will have a magnification between 0 and 1:

  • 0 < M < 1 .

• Negative magnifications represent a virtual image (discussed in another lesson).

Proper Format for Science Word Problems

• G Given: List all information using symbols.

• R Required: What do we need to solve for? Use symbols.

• A Analyze: Write out the proper formula.

• S Solve: Insert numbers into the formula and calculate.

• S Sentence: Summarize the answer.

• Some instructors may use the acronym GRASP instead.

Example Problem 1a

• Problem statement:

  • A concave mirror produces an image on a wall that is 30.0 cm high from an object that is 6.5 cm high. What is the magnification of the mirror?

Breakdown:

1. Given:

   • h_i = 30.0 \, cm

   • h_o = 6.5 \, cm

2. Required:

   • M $?

3. Analyze:

   • Use the formula: M = \frac{hi}{ho}

4. Solve:

   • Insert values into formula:

   • M = \frac{30.0 \, cm}{6.5 \, cm} = 4.6

5. Sentence:

   • The magnification is 4.6 times larger.

   • Note: There are no units for magnification except for "times."

Example Problem 1b

• Problem statement:

  • A microscope produces an image 1.00 x 10^-4 m high from an object 4.00 x 10^-7 m high. What is the magnification of the microscope?

Breakdown:

1. Given:

   • h_i = 1.00 \times 10^{-4} \, m

   • h_o = 4.00 \times 10^{-7} \, m

2. Required:

   • M = ?

3. Analyze:

   • Use the formula: M = \frac{hi}{ho}

4. Solve:

   • M = \frac{1.00 \times 10^{-4} \, m}{4.00 \times 10^{-7} \, m} = 250

5. Sentence:

   • The magnification is 250 times.

Example Problem 2a

• Problem statement:

  • A concave mirror creates a real image 16.0 cm from its surface. The image is formed 4 times larger; how far away is the object?

Breakdown:

1. Given:

   • d_i = 16.0 \, cm

   • M = 4

2. Required:

   • d_o = ?

3. Analyze:

   • Use the formula: do = \frac{di}{M}

4. Solve:

   • d_o = \frac{16.0 \, cm}{4} = 4 \, cm

5. Sentence:

   • The object is located 4 cm from the mirror.

Example Problem 2b

• Problem statement:

  • A concave mirror creates a virtual image of a candle flame that is 10 cm high. If the magnification is 12.5, what is the height of the candle flame?

Breakdown:

1. Given:

   • h_i = 10 \, cm

   • M = 12.5

2. Required:

   • h_o = ?

3. Analyze:

   • Use the formula: ho = \frac{hi}{M}

4. Solve:

   • h_o = \frac{10 \, cm}{12.5} = 0.8 \, cm

5. Sentence:

   • The candle flame is 0.8 cm high.

You Try It!

• Note: Each question is worth 5 marks but must be done fully; otherwise, marks will be deducted.

• Complete all work.

• Remember relationships: hi = di \, ho = do