$A$ plano-convex lens is made of a material of refractive index $n$. When a small object is placed $30 \ cm$ away in front of the curved surface of the lens,an image of double the size of the object is produced. Due to reflection from the curved surface of the lens,another faint image is observed at a distance of $10 \ cm$ away from the lens. Which of the following statement$(s)$ is(are) true?
$(A)$ The refractive index of the lens is $2.5$
$(B)$ The radius of curvature of the convex surface is $45 \ cm$
$(C)$ The faint image is erect and real
$(D)$ The focal length of the lens is $20 \ cm$
$(A)$ The refractive index of the lens is $2.5$
$(B)$ The radius of curvature of the convex surface is $45 \ cm$
$(C)$ The faint image is erect and real
$(D)$ The focal length of the lens is $20 \ cm$
- A$A, B$
- B$A, D$
- C$A, C$
- D$B, D$
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View SolutionThe exposure time of a camera lens at the $f/2.8$ setting is $1/200$ second. The correct time of exposure at $f/5.6$ is......$sec$
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View SolutionAn optical arrangement consists of two concave mirrors $M_1$ and $M_2$,and a convex lens $L$ with a common principal axis,as shown in the figure. The focal length of $L$ is $10 \text{ cm}$. The radii of curvature of $M_1$ and $M_2$ are $20 \text{ cm}$ and $24 \text{ cm}$,respectively. The distance between $L$ and $M_2$ is $20 \text{ cm}$. $A$ point object $S$ is placed at the mid-point between $L$ and $M_2$ on the axis. When the distance between $L$ and $M_1$ is $n/7 \text{ cm}$,one of the images coincides with $S$. The value of $n$ is. . . .
Define a ray and a beam of light.
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View SolutionMatch List $I$ with List $II$ and select the correct answer using the codes given below the lists:
List $I$ (Position of the object) List $II$ (Magnification) $(I)$ An object is placed at focus before a convex mirror $(A)$ Magnification is $-\infty$ $(II)$ An object is placed at centre of curvature before a concave mirror $(B)$ Magnification is $0.5$ $(III)$ An object is placed at focus before a concave mirror $(C)$ Magnification is $+1$ $(IV)$ An object is placed at centre of curvature before a convex mirror $(D)$ Magnification is $-1$ $(E)$ Magnification is $0.33$
| List $I$ (Position of the object) | List $II$ (Magnification) |
|---|---|
| $(I)$ An object is placed at focus before a convex mirror | $(A)$ Magnification is $-\infty$ |
| $(II)$ An object is placed at centre of curvature before a concave mirror | $(B)$ Magnification is $0.5$ |
| $(III)$ An object is placed at focus before a concave mirror | $(C)$ Magnification is $+1$ |
| $(IV)$ An object is placed at centre of curvature before a convex mirror | $(D)$ Magnification is $-1$ |
| $(E)$ Magnification is $0.33$ |
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