Difficult
An object is placed at a distance of $100 \text{ cm}$ from a converging lens of focal length $40 \text{ cm}$. $(i)$ What is the nature of the image? (ii) What is the position of the image? A convex lens produces an inverted image magnified three times of an object placed at a distance of $15 \text{ cm}$ from it. Calculate the focal length of the lens.
(N/A) Part $1$: Given $u = -100 \text{ cm}$, $f = +40 \text{ cm}$.
Using lens formula $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$:
$\frac{1}{v} - \frac{1}{-100} = \frac{1}{40} \implies \frac{1}{v} = \frac{1}{40} - \frac{1}{100} = \frac{5-2}{200} = \frac{3}{200}$.
$v = \frac{200}{3} \approx 66.67 \text{ cm}$. Since $v$ is positive, the image is real and inverted.
Part $2$: Given $u = -15 \text{ cm}$, magnification $m = -3$ (inverted image).
$m = \frac{v}{u} \implies -3 = \frac{v}{-15} \implies v = 45 \text{ cm}$.
Using $\frac{1}{f} = \frac{1}{v} - \frac{1}{u} = \frac{1}{45} - \frac{1}{-15} = \frac{1+3}{45} = \frac{4}{45}$.
$f = \frac{45}{4} = 11.25 \text{ cm}$.
Using lens formula $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$:
$\frac{1}{v} - \frac{1}{-100} = \frac{1}{40} \implies \frac{1}{v} = \frac{1}{40} - \frac{1}{100} = \frac{5-2}{200} = \frac{3}{200}$.
$v = \frac{200}{3} \approx 66.67 \text{ cm}$. Since $v$ is positive, the image is real and inverted.
Part $2$: Given $u = -15 \text{ cm}$, magnification $m = -3$ (inverted image).
$m = \frac{v}{u} \implies -3 = \frac{v}{-15} \implies v = 45 \text{ cm}$.
Using $\frac{1}{f} = \frac{1}{v} - \frac{1}{u} = \frac{1}{45} - \frac{1}{-15} = \frac{1+3}{45} = \frac{4}{45}$.
$f = \frac{45}{4} = 11.25 \text{ cm}$.
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Similar Questions
$(a)$ Define absolute refractive index.
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$(i)$ Which of the three media $A, B$ or $C$ has maximum optical density?
$(ii)$ Through which of the three media,will the speed of light be maximum?
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$(b)$ The path of a light ray from three different media $A, B$ and $C$ for a given angle of incidence is shown below. Study the diagrams and answer the following questions.
$(i)$ Which of the three media $A, B$ or $C$ has maximum optical density?
$(ii)$ Through which of the three media,will the speed of light be maximum?
$(iii)$ Will the light travelling from $A$ to $B$ bend towards or away from the normal?
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Medium
View Solution$A$ point object emits rays in all directions. Consider a ray emitted from the object that is parallel to the principal axis of the mirror. One of the points required to trace the reflected ray is the point of incidence itself,as shown in the figure. Select a point from the given figure through which the reflected ray passes.
Study the given ray diagrams and select the correct statement from the following:
$(A)$ Device $X$ is a concave mirror and device $Y$ is a convex lens, whose focal lengths are $20 \text{ cm}$ and $25 \text{ cm}$ respectively.
$(B)$ Device $X$ is a convex lens and device $Y$ is a concave mirror, whose focal lengths are $10 \text{ cm}$ and $25 \text{ cm}$ respectively.
$(C)$ Device $X$ is a concave lens and device $Y$ is a convex mirror, whose focal lengths are $20 \text{ cm}$ and $25 \text{ cm}$ respectively.
$(D)$ Device $X$ is a convex lens and device $Y$ is a concave mirror, whose focal lengths are $20 \text{ cm}$ and $25 \text{ cm}$ respectively.
$(A)$ Device $X$ is a concave mirror and device $Y$ is a convex lens, whose focal lengths are $20 \text{ cm}$ and $25 \text{ cm}$ respectively.
$(B)$ Device $X$ is a convex lens and device $Y$ is a concave mirror, whose focal lengths are $10 \text{ cm}$ and $25 \text{ cm}$ respectively.
$(C)$ Device $X$ is a concave lens and device $Y$ is a convex mirror, whose focal lengths are $20 \text{ cm}$ and $25 \text{ cm}$ respectively.
$(D)$ Device $X$ is a convex lens and device $Y$ is a concave mirror, whose focal lengths are $20 \text{ cm}$ and $25 \text{ cm}$ respectively.
MediumCBSE 2017
View Solution$(a)$ To construct a ray diagram, we use two rays chosen such that their directions after reflection from the mirror are easily determined. List two such rays and state the path of these rays after reflection for a concave mirror. Use these two rays to draw a ray diagram to locate the image of an object placed between the pole and the focus of a concave mirror.
$(b)$ $A$ concave mirror produces a three-times magnified image on a screen. If the object is placed $20 \text{ cm}$ in front of the mirror, how far is the screen from the object?
$(b)$ $A$ concave mirror produces a three-times magnified image on a screen. If the object is placed $20 \text{ cm}$ in front of the mirror, how far is the screen from the object?
DifficultCBSE 2017
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Medium
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