A student focused the image of a candle flame on a white screen by placing the flame at various distances from a convex lens. He noted his observation as given below:

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7.5 cm

6.5 cm

9.5 cm

5.5 cm

answer is A.

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Detailed Solution

Concept- The focal length of a lens is its length. The focal length is the distance between the focus and the mirror's pole. The focal length of the lens can be simply determined using the given observation values and the lens formula, as well as suitable sign conventions. Distances measured from the lens's pole, measured in the opposite direction of the incident ray, are negative, whereas distances measured in the same direction as the incident ray are positive, according to the sign convention.
The following formula was used:
The following is the lens formula:

The focal length is f, the image distance is v, and the object distance is u. Sign conventions that are correct should be adhered to while changing the values.
The focal length of a lens refers to the distance between the focus and the pole of the mirror. After applying suitable sign conventions to the variables in the table, we can feed them into the lens formula to get the focal length of the lens.
The following is the sign convention:
It means that distances measured in the direction of the incident ray from the lens's pole should be regarded as negative, while distances measured in the direction of the incident ray should be considered positive. The object distance is almost often assumed to be negative. As a result, u is negative. A convex lens generates a true picture on the opposite side of the lens since it is a converging lens (the side opposite to the one from which the incident ray is coming) .
As a result, the image distance is always positive and in the direction of the incident beam. As a result, v is positive.
The following is the lens formula:

The focal length is f, the image distance is v, and the object distance is u. When substituting values, proper sign convention should be used. With this knowledge, we can calculate the focus length using any observation data. Take, for example, observation 1.
Here,

Putting these values in the lens formula (1) , we get,

As a result, the lens' focal length is

.
Hence, option 1 is the correct answer.

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