Question 14 Marks
Study the following table for a convex lens for different positions of object and answer the following questions:
| Position of object | Position of image | Relative size of image |
| At infinity | At focus F_(2) | Highly diminished point sized |
| Beyond 2F_(1) | Between F_(2) and 2F_(2) | Diminished |
| At 2F_(1) | At 2F_(2) | Same size |
| Between F_(1) and 2F_(1) | Beyond 2F_(2) | Enlarged |
| At focus F_(1) | At infinity | Infinitely large or highly enlarged |
| Between focus F_(1) and optical centre O | On the same side of the lens as the object | Enlarged |
(i) What is the nature of the image, if an object is placed at infinity ?
(ii) Identify the nature of the image for which the object is between focus and optical centre.
(iii) What is position of image, when object is place at focus $\left(f_1\right)$ ?
or
(iv) What is the focal length of a lens for an object placed $50 cm$ from the lens producing virtual image at a distance of $10 cm$ in front of the lens?
Answer
View full question & answer→(i) When the object is at infinity, nature of the image will be real, inverted, highly diminished, point sized.
(ii) Virtual and erect
(ii) Infinity
(iv) Given,
Object distance, $\quad u=-50 cm$
Image distance, $\quad v=-10 cm$
As we know that,
\[\begin{aligned}\frac{1}{v}-\frac{1}{u} & =\frac{1}{f} \\-\frac{1}{10}-\frac{1}{-50} & \frac{1}{f} \\\frac{-5+1}{50} & =\frac{1}{f} \\f & =-\frac{50}{4} \\& =-12.5 cm\end{aligned}\]
(ii) Virtual and erect
(ii) Infinity
(iv) Given,
Object distance, $\quad u=-50 cm$
Image distance, $\quad v=-10 cm$
As we know that,
\[\begin{aligned}\frac{1}{v}-\frac{1}{u} & =\frac{1}{f} \\-\frac{1}{10}-\frac{1}{-50} & \frac{1}{f} \\\frac{-5+1}{50} & =\frac{1}{f} \\f & =-\frac{50}{4} \\& =-12.5 cm\end{aligned}\]
