Unlocking the Secrets of Magnification and Power

Have you ever wondered how a magnifying glass works?

Considering a magnifying glass that produces a magnification of 3.00 when held 6.5 cm from an object, such as a rare coin, what is the focal length of the magnifying glass? And how can we calculate the power of the magnifier in diopters?

Understanding Magnification and Power

The focal length of the magnifying glass is 15.00 cm, and the power of the magnifier is 0.067 D.

Have you ever marveled at how a magnifying glass can bring tiny details into sharp focus? Understanding the science behind magnification and power can help us appreciate the wonders of optics even more.

Calculating the Focal Length

To find the focal length of the magnifying glass, we can use the magnification formula:

Magnification = - (image distance / object distance) = - (d_i / d_o)

Given that the magnification is 3.00 and the object is held 6.5 cm from the magnifying glass, we can plug in these values into the formula:

3.00 = - (d_i / 6.5)

Solving for the image distance, we get:

d_i = - 3.00 * 6.5 = -19.5 cm

The focal length is the distance from the lens to the image, and since the image is formed on the same side as the object, the focal length is positive. Therefore, the focal length of the magnifying glass is 19.5 cm.

Calculating the Power

The power of a lens is given by the formula:

Power = 1 / focal length

Using the focal length calculated, we can find the power:

Power = 1 / 19.5 = 0.051 D (rounded to three significant figures)

By understanding the concepts of magnification and power, we can unlock the secrets of how magnifying glasses work and appreciate the intricate science behind everyday objects.