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  • An experiment is conducted to determine the focal length  of a convex lens using a traveling microscope. The micr

An experiment is conducted to determine the focal length (f) of a convex lens using a traveling microscope. The microscope is mounted vertically, and a distant object is focused using the microscope’s crosswire. The distance between the object and the microscope is measured to be D=20\ cm. The object is then replaced with the convex lens, and the microscope is focused on the image formed by the lens. The microscope reading is found to be R=3\ cm. Given that the least count of the traveling microscope is 0.01\ cm, calculate the focal length of the convex lens.

Option: 1

(2.53 \pm 0.005) \mathrm{cm}


Option: 2

(3.53 \pm 0.005) \mathrm{cm}


Option: 3

(3.53 \pm 0.001) \mathrm{cm}


Option: 4

(3.53 \pm 0.002) \mathrm{cm}


Answers (1)

best_answer

Given values:
• Distance between object and microscope (D)=20\ cm
• Microscope reading (R)=3\ cm
• Least count of the traveling microscope =0.01\ cm
The focal length (f) of the convex lens can be calculated using the formula:

f=\frac{R \times D}{D-R}
Step 1: Calculate the numerator and denominator:
Numerator \mathrm{}=R \times D=3 \mathrm{~cm} \times 20 \mathrm{~cm}=60 \mathrm{~cm}^2 \mathrm{}
Denominator \mathrm{}=D - R=20 \mathrm{~cm} -3 \mathrm{~cm}=17 \mathrm{~cm} \mathrm{} 
Step 2: Substitute the values and calculate the focal length (f):

f=\frac{60 \mathrm{~cm}^2 \mathrm{~cm}}{17 \mathrm{~cm}} \approx 3.53 \mathrm{~cm}

Step 3: Calculate the uncertainty in the focal length due to least count:
Uncertainty in f=\frac{\text { Least count }}{2}=\frac{0.01 \mathrm{~cm}}{2}=0.005 \mathrm{~cm}

Step 4: Express the result with uncertainty:
f=(3.53 \pm 0.005) \mathrm{cm}

The focal length of the convex lens is approximately 3.53\ cm with an uncertainty of 0.05\ cm

So, option B is correct

Posted by

Ritika Kankaria

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