Optics 3 Question 37
37. An image $Y$ is formed of point object $X$ by a lens whose optic axis is $A B$ as shown in figure. Draw a ray diagram to locate the lens and its focus. If the image $Y$ of the object $X$ is formed by a concave mirror (having the same optic axis as $A B$ ) instead of lens, draw another ray diagram to locate the mirror and its focus. Write down the steps of construction of the ray diagrams.
$(1994,6 M)$
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Answer:
Correct Answer: 37. See the hints
Solution:
- Steps I In case of a lens
(a) Join $X$ and $Y$. The point $O$, where the line $X Y$ cuts the optic axis $A B$, is the optical centre of the lens.
(b) Draw a line parallel to $A B$ from point $X$. Let it cuts the lens at $L$. Join $L$ and $Y$. The point $F$ where the line $L Y$ cuts the optic axis $A B$ is the focus of the lens $F$.
NOTE
As the image is inverted, lens should be a convex because a concave lens always forms a virtual and erect image.
Step II In case of a concave mirror
(a) Draw a line $Y Y^{\prime}$ perpendicular to $A B$ from point $Y$. Let it cuts the line $A B$ at point $P$. Locate a point $Y^{\prime}$ such that $P Y=P Y^{\prime}$.
(b) Extend the line $X Y^{\prime}$. Let it cuts the line $A B$ at point $O$. Then $O$ is the pole of the mirror.
(c) Join $X$ and $Y$. The point $C$, where the line $X Y$ cuts the optic axis $A B$, is the centre of curvature of the mirror.
(d) The centre point $F$ of $O C$ is the focus of the mirror.
