Question

. u' तथा 'V' के बीच ग्राफ खींचकर उत्तल लेन्स की फोकस दूरी ज्ञात करें। Find the focal length of convex lens by plotting graph between 'u' and 'v'.​

Answer 1

To find the focal length of a convex lens by plotting graphs between u and we have to undertake the following experiment:

we  will require the following apparatus:

• an optical bench
• a Metre scale
• two iron nails
• Three uprights (with clamps)
• A convex lens of preferably  focal length less than 20 cm

Theory:

"For a body positioned at a distance ‘u’ from the optical center of a thin convex lens of focal length ‘f’, an inverted and real image is generated on the lens’s other side at a distance ‘v’ from the optical center."

we can note that the relationship between these quantities as:

$\frac{1}{f} =\frac{1}{v} -\frac{1}{u}$

So, the focal length is,

$\frac{1}{f} =\frac{u-v}{uv}$

$f =\frac{uv}{u-v}$

Procedure:

• Fix the convex lens in the holder.

• then focus an object like a tree on a white screen
• Precisely focus the image of the object on the white screen until a sharp image is obtained.
• measure the distance between the lens and the wall or screen. It is the approximate focal length of the lens.
• Mount the holder with the lens in a locked upright, and place the upright at the 50cm mark.
• adjust the lens in such a way that it is perpendicular and vertical to the optical bench.
• Use the thin optical needle as the object (O). Fix it in the outer, laterally movable upright close to zero ends.
• Adjust the object needle upright, and place it at a distance close to 1.5 times the acquired approximate focal length of the lens.
• adjust the height of the object needle to adjust its tip to lie on the horizontal plane through the lens’s optical center.
• Record the position of the index mark on the foot of the object needle upright.
• with one eye open, watch from the other end of the optical bench. The image’s tip should be seen in the middle of the lens.
• Position the thick optical image needle in the fourth upright close to the other terminal of the optical bench.
• adjust the height of the imaging needle in a way that its tip is visible in line with the image’s tip when seen with one eye open.
• Look towards the right. The tips will be separated. The image needle tip and the image tip may differ in position. Clear the difference tip to tip.
• Record the position of the index mark on the foot of the image needle upright.
• Note down the position of the index mark on the foot of the upright of lens, the image needle, and the object needle in the second observation column.
• find out the index correction for the length between the tip of the object needle and the optical center of the lens. Next, find the distance between the tip of the image needle and the optical center of the lens, as mentioned.
• Adjust the object needle upright towards the mirror in steps 1cm to obtain observations 1 and 2. Repeat the process.
• Note down the observations.

in this way, we can find the focal length of the convex lens by plotting graph between 'u' and 'v'.​

please refer to the attached diagram:

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