How To Calculate Magnification 12 Steps With Pictures

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.

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. [5] X Research source

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.

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.

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

In the equation, fo refers to the focal length of the objective lens and fe to the focal length of the eyepiece lens. The objective lens is the large lens at the end of the device, while the eyepiece lens is, as its name suggests, the small lens you put your eye next to.

For example, let’s say that we have a small telescope. If the focal length of the objective lens is 10 centimeters and the focal length of the eyepiece lens is 5 centimeters, the magnification is simply 10/5 = 2.

For example, let’s say that we have the same setup as in our example problem in Method 1: a six-inch action figure 50 centimeters away from a converging lens with a focal length of 20 centimeters. Now, let’s put a second converging lens with a focal length of 5 centimeters 50 centimeters behind the first lens (100 centimeters away from the action figure. ) In the next few steps, we’ll use this information to find the magnification of the final image.

From our work in Method 1 above, we know that the first lens produces an image -3. 996 centimeters high, 33. 3 centimeters behind the lens, and with a magnification of -0. 666.

In our example, since the image is 33. 3 centimeters behind the first lens, it is 50-33. 3 = 16. 7 centimeters in front of the second one. Let’s use this and the new lens’s focal length to find the second lens’s image. 1/f = 1/do + 1/di 1/5 = 1/16. 7 + 1/di 0. 2 - 0. 0599 = 1/di 0. 14 = 1/di di = 7. 14 centimeters Now, we can find hi and M for the second lens: (hi/ho) = -(di/do) (hi/-3. 996) = -(7. 14/16. 7) hi = -(0. 427) × -3. 996 hi = 1. 71 centimeters M = (hi/ho) M = (1. 71/-3. 996) = -0. 428

Keep in mind that subsequent lenses can continue to invert your image. For instance, the magnification value we got above (-0. 428) indicates that the image we see will be about 4/10 the size of the image from the first lens, but right side up, since the image from the first lens was upside down.