How to Calculate Magnification
Start with your equation and determine which variables you know., Use the lens equation to get di., Solve for hi., Solve for M. You can solve for your final variable using either -(di/do) or (hi/ho)., Interpret your M value., For diverging lenses...
Step-by-Step Guide
-
Step 1: Start with your equation and determine which variables you know.
Like with many other physics problems, a good way to approach magnification problems is to first write the equation you need to find your answer.
From here, you can work backwards to find any pieces of the equation that you need.
For example, let's say that a 6 centimeter tall action figure is placed half a meter away from a converging lens with a focal length of 20 centimeters.
If we want to find the magnification, image size, and image distance, we can start by writing our equation like this:
M = (hi/ho) =
-(di/do) Right now, we know ho (the height of the action figure) and do (the distance of the action figure from the lens.) We also know the focal length of the lens, which isn't in this equation.
We need to find hi, di, and M. -
Step 2: Use the lens equation to get di.
If you know the distance of the object you're magnifying from the lens and the focal length of the lens, finding the distance of the image is easy with the lens equation.
The lens equation is 1/f = 1/do + 1/di, where f = the focal length of the lens.
In our example problem, we can use the lens equation to find di.
Plug in your values for f and do and solve: 1/f = 1/do + 1/di 1/20 = 1/50 + 1/di 5/100
- 2/100 = 1/di 3/100 = 1/di 100/3 = di =
33.3 centimeters A lens's focal length is the distance from the center of the lens to the point where the rays of light converge in a focal point.
If you've ever focused light through a magnifying glass to burn ants, you've seen this.
In academic problems, this is often given to you.
In real life, you can sometimes find this information labeled on the lens itself., Once you know do and di, you can find the height of the magnified image and the magnification of the lens.
Notice the two equals signs in the magnification equation (M = (hi/ho) =
-(di/do)) — this means that all of the terms are equal to each other, so we can find M and hi in whatever order we want.
For our example problem, we can find hi like this: (hi/ho) =
-(di/do) (hi/6) =
-(33.3/50) hi =
-(33.3/50) × 6 hi =
-3.996 cm Note that a negative height indicates that the image we see will be inverted (upside down). , In our example, we would finally find M like this:
M = (hi/ho) M = (-3.996/6) =
-0.666 We also get the same answer if we use our d values:
M =
-(di/do) M =
-(33.3/50) =
-0.666 Note that magnification does not have a unit label. , Once you have a magnification value, you can predict several things about the image you would view through the lens.
These are:
Its size.
The bigger the absolute value of the M value, the bigger the object will seem under magnification.
M values between 1 and 0 indicate that the object will look smaller.
Its orientation.
Negative values indicate that the image of the object will be inverted.
In our example, our M value of
-0.666 means that, under the conditions given, the image of the action figure will appear upside down and two-thirds its normal size. , Even though diverging lenses look very different than converging lenses, you can find their magnification values using the same formulas as above.
The one important exception here is that divergent lenses will have negative focal lengths.
In a problem like the one above, this will affect the answer you get for di, so be sure to pay close attention.
Let's re-do the example problem above, only this time, we'll say we're using a diverging lens with a focal length of
-20 centimeters.
All of the other starting values are the same.
First, we'll find di with the lens equation: 1/f = 1/do + 1/di 1/-20 = 1/50 + 1/di
-5/100
- 2/100 = 1/di
-7/100 = 1/di
-100/7 = di =
-14.29 centimeters Now we'll find hi and M with our new di value. (hi/ho) =
-(di/do) (hi/6) =
-(-14.29/50) hi =
-(-14.29/50) × 6 hi =
1.71 centimeters M = (hi/ho) M = (1.71/6) =
0.285 -
Step 3: Solve for hi.
-
Step 4: Solve for M. You can solve for your final variable using either -(di/do) or (hi/ho).
-
Step 5: Interpret your M value.
-
Step 6: For diverging lenses
-
Step 7: use a negative focal length value.
Detailed Guide
Like with many other physics problems, a good way to approach magnification problems is to first write the equation you need to find your answer.
From here, you can work backwards to find any pieces of the equation that you need.
For example, let's say that a 6 centimeter tall action figure is placed half a meter away from a converging lens with a focal length of 20 centimeters.
If we want to find the magnification, image size, and image distance, we can start by writing our equation like this:
M = (hi/ho) =
-(di/do) Right now, we know ho (the height of the action figure) and do (the distance of the action figure from the lens.) We also know the focal length of the lens, which isn't in this equation.
We need to find hi, di, and M.
If you know the distance of the object you're magnifying from the lens and the focal length of the lens, finding the distance of the image is easy with the lens equation.
The lens equation is 1/f = 1/do + 1/di, where f = the focal length of the lens.
In our example problem, we can use the lens equation to find di.
Plug in your values for f and do and solve: 1/f = 1/do + 1/di 1/20 = 1/50 + 1/di 5/100
- 2/100 = 1/di 3/100 = 1/di 100/3 = di =
33.3 centimeters A lens's focal length is the distance from the center of the lens to the point where the rays of light converge in a focal point.
If you've ever focused light through a magnifying glass to burn ants, you've seen this.
In academic problems, this is often given to you.
In real life, you can sometimes find this information labeled on the lens itself., Once you know do and di, you can find the height of the magnified image and the magnification of the lens.
Notice the two equals signs in the magnification equation (M = (hi/ho) =
-(di/do)) — this means that all of the terms are equal to each other, so we can find M and hi in whatever order we want.
For our example problem, we can find hi like this: (hi/ho) =
-(di/do) (hi/6) =
-(33.3/50) hi =
-(33.3/50) × 6 hi =
-3.996 cm Note that a negative height indicates that the image we see will be inverted (upside down). , In our example, we would finally find M like this:
M = (hi/ho) M = (-3.996/6) =
-0.666 We also get the same answer if we use our d values:
M =
-(di/do) M =
-(33.3/50) =
-0.666 Note that magnification does not have a unit label. , Once you have a magnification value, you can predict several things about the image you would view through the lens.
These are:
Its size.
The bigger the absolute value of the M value, the bigger the object will seem under magnification.
M values between 1 and 0 indicate that the object will look smaller.
Its orientation.
Negative values indicate that the image of the object will be inverted.
In our example, our M value of
-0.666 means that, under the conditions given, the image of the action figure will appear upside down and two-thirds its normal size. , Even though diverging lenses look very different than converging lenses, you can find their magnification values using the same formulas as above.
The one important exception here is that divergent lenses will have negative focal lengths.
In a problem like the one above, this will affect the answer you get for di, so be sure to pay close attention.
Let's re-do the example problem above, only this time, we'll say we're using a diverging lens with a focal length of
-20 centimeters.
All of the other starting values are the same.
First, we'll find di with the lens equation: 1/f = 1/do + 1/di 1/-20 = 1/50 + 1/di
-5/100
- 2/100 = 1/di
-7/100 = 1/di
-100/7 = di =
-14.29 centimeters Now we'll find hi and M with our new di value. (hi/ho) =
-(di/do) (hi/6) =
-(-14.29/50) hi =
-(-14.29/50) × 6 hi =
1.71 centimeters M = (hi/ho) M = (1.71/6) =
0.285
About the Author
Joan Parker
Dedicated to helping readers learn new skills in crafts and beyond.
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