## Power of Lens and Measurement of Focal Length

Subject: Physics

#### Overview

This note provides us with an information about the power of lens and measurement of focal length .The power of a lens is a measure of its ability to produce the deviation of light. A lens of short focal length produces more deviation of light than that of a lens of larger focal length. So, power of a lens is defined as the reciprocal of its focal length

#### Power of Lens

The power of a lens is a measure of its ability to produce deviation of light. A lens of short focal length produces more deviation of light than that of a lens of larger focal length. So, power of a lens is defined as the reciprocal of its focal length. The unit of power of lens is dioptre, D where f is in meter.

$$\text {Power of a lens, P} = \frac 1f$$

P = 1 dioptre if f = 1 m. thus power of a lens is 1D if its focal length is 1m. when more than two lenses are placed in contact, the combined power is given by

\begin{align*} P &= \frac {1}{f_1} + \frac {1}{f_2} + \frac {1}{f_3} \dots \\ &= P_1 + P_2 + P_3 + \dots \\ \end{align*}

The proper sign of individual must be taken while calculating the power. P is positive for convex lens and negative for concave lens depending on sign of F’.

#### Magnification

The linear magnification of a lens is defined as the ratio of the size of image produced by it to the size of object. In general,

\begin{align*} \text {magnification,} \: m &= \frac {\text {size of image}}{\text {size of object}} \\ \text {or,} \: m &= \frac {\text {height of image}}{\text {height of object}} \\ \end{align*}

Consider an object OP beyond focus of a convex lens. Two rays PS and PC meet after refraction through the lens at Q. IQ is the real image of the object OP.

From the figure, we see that two triangles POC and QIC are similar triangle. So,

\begin{align*} \frac {IQ}{OP} &= \frac {IC}{OC} \\ \text {or,} \: m &= \frac vu \\ \end{align*}

where v is the image distance and u is the object distance. If the image is real, the magnification of the lens is taken as positive while if the image is virtual, the magnification is taken as negative.

#### Measurement of Focal Length

1. Convex Lens
The focal length of a convex lens can be measured by u-v method. First of all, the rough focal length of the given convex lens is measured by focusing a distance object on wall or on a screen. The distance between the lens and the screen is the focal length of the lens. Now, the lens is mounted with a stand at the middle of optical bench as shown in the figure. The object pin is mounted at one side of the bench at a distance greater than 2f from the lens. The image pin is mounted at the other side of the bench. The image of the object pin is inverted and tip of the image lies over the tip of the image pin. By trial and error method, the parallax is removed between the object and the image. Noting the positions of pins, the object distance and the image distance are measured. Several pair of such distances are measured and putting these values in lens formula $\frac 1f = \frac 1u + \frac 1v$ we can calculate the focal length.
2. Concave lens
The focal length of a concave lens can be measured by using a convex lens. A convex lens M of known focal length is mounted on the optical bench. At one side of the bench, an object pin at greater distance than the focal length of M is fixed and the exact position of the image is found at O as shown in the figure where another pin is fixed. Now, between the image pin O and M, a concave lens is introduced on a stand and since the converging light beam is incident on the concave lens, O acts as a virtual object. As the concave lens diverges the light rays, the image is formed at I farther from the lens. A pin is fixed at I and its position is noted after removing the parallax between the two pins at O and I. after noting the position of M, O and I, the distance OL and IL can be measured. So, object distance, u =- LO and image distance, v = LI. By putting the values of u and v, we can calculate the value of focal length of the concave lens.
##### Things to remember
• \begin{align*} P &= \frac {1}{f_1} + \frac {1}{f_2} + \frac {1}{f_3} \dots \\ &= P_1 + P_2 + P_3 + \dots \\ \end{align*}
• The linear magnification of a lens is defined as the ratio of the size of image produced by it to the size of object. In general,
• The focal length of a convex lens can be measured by u-v method
• The focal length of a concave lens can be measured by using a convex lens
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