Medium
Study the following table for a convex lens for different positions of the 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 when the object is between the focus and the optical centre.
(iii) What is the position of the image when the object is placed at focus $F_1$?
(iv) What is the focal length of a lens for an object placed $50 \text{ cm}$ from the lens producing a virtual image at a distance of $10 \text{ cm}$ in front of the lens?
| 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 when the object is between the focus and the optical centre.
(iii) What is the position of the image when the object is placed at focus $F_1$?
(iv) What is the focal length of a lens for an object placed $50 \text{ cm}$ from the lens producing a virtual image at a distance of $10 \text{ cm}$ in front of the lens?
(N/A) $(i)$ When the object is at infinity, the image is real, inverted, and highly diminished (point-sized).
(ii) When the object is between the focus $F_1$ and the optical centre $O$, the image is virtual and erect.
(iii) When the object is at focus $F_1$, the image is formed at infinity.
(iv) Given:
Object distance $u = -50 \text{ cm}$
Image distance $v = -10 \text{ cm}$ (virtual image is formed on the same side as the object).
Using the lens formula: $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$
$\frac{1}{-10} - \frac{1}{-50} = \frac{1}{f}$
$-\frac{1}{10} + \frac{1}{50} = \frac{1}{f}$
$\frac{-5 + 1}{50} = \frac{1}{f}$
$-\frac{4}{50} = \frac{1}{f}$
$f = -12.5 \text{ cm}$
(ii) When the object is between the focus $F_1$ and the optical centre $O$, the image is virtual and erect.
(iii) When the object is at focus $F_1$, the image is formed at infinity.
(iv) Given:
Object distance $u = -50 \text{ cm}$
Image distance $v = -10 \text{ cm}$ (virtual image is formed on the same side as the object).
Using the lens formula: $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$
$\frac{1}{-10} - \frac{1}{-50} = \frac{1}{f}$
$-\frac{1}{10} + \frac{1}{50} = \frac{1}{f}$
$\frac{-5 + 1}{50} = \frac{1}{f}$
$-\frac{4}{50} = \frac{1}{f}$
$f = -12.5 \text{ cm}$
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