question_answer

Analyse the following observation table showing variation of image-distance (v) with object distance (u) in case of a convex lens and answer the questions that follow without doing any calculations:
S. No.	Object - Distance u (cm)	Image - Distance v (cm)
1.	\[\text{ }100\]	\[+\text{ }25\]
2.	\[\text{ }60\]	\[+\text{ }30\]
3.	\[\text{ }40\]	\[+\text{ }40\]
4.	\[\text{ }30\]	\[+\text{ }60\]
5.	\[\text{ }25\]	\[+\text{ }100\]
6.	\[\text{ }15\]	\[+\text{ }120\]
(a) What is the focal length of the convex lens? Give reason to justify your answer.
(b) Write the serial number of the observation which is not correct. On what basis have you arrived at this conclusion?
(c) Select an appropriate scale and draw a ray diagram for the observation at S. No. 2. Also find the approximate value of magnification.

 

Answer:

(a) From the observation 3, the radius of curvature of the lens is 40 cm as distance of object and the distance of the image is same.

\[\therefore \]      Focal length, \[f=\frac{R}{2}=\frac{40}{2}=20cm\]

(b) S. No. 6 is not correct, as for this observation the object distance is between focus and pole and for such case, the image formed is always virtual, but in this case real image is forming as the image distance is positive.

(c)

\[\text{Magnification=}\frac{v}{u}=\frac{+\,30\,cm}{-\,60\,cm}=-0.5\]