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:

  • $M = \frac{h<em>i}{h</em>o}$

  • Where:

    • $M$ = Magnification

    • $h_i$ = Height of the image

    • $h_o$ = Height of the object

• Rearranged forms include:

  • $h<em>i = h</em>o \times M$

  • $h<em>o = \frac{h</em>i}{M}$

Magnification Formula for Distances

• Use the formula:

  • $M = \frac{d<em>i}{d</em>o}$

  • Where:

    • $d_i$ = Image distance

    • $d_o$ = Object distance

• Rearranged forms include:

  • $d<em>i = d</em>o \times M$

  • $d<em>o = \frac{d</em>i}{M}$

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: $M = \frac{h<em>i}{h</em>o}$

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: $M = \frac{h<em>i}{h</em>o}$

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: $d<em>o = \frac{d</em>i}{M}$

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: $h<em>o = \frac{h</em>i}{M}$

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: $h<em>i = d</em>i \, h<em>o = d</em>o$