Lens Formula

Q. An object and its real image are located at distances $25\text{cm}$ and $40\text{cm}$ respectively from the two principal focii of a convex lens on either side. The linear magnification of the image is nearly equal to

1. $+1.3$
2. $-1.3$
3. $+1.8$
4. $-1.8$

Q. A thin convex lens made from crown glass $(\mu =\frac{3}{2})$ has focal length f. When it is measured in two different liquids having refractive indices $\frac{4}{3}and\frac{5}{3}$, it has the focal lengths $f_{1}and{f}_2$ respectively. The correct relation between the focal lengths is:

1. $f_2>fand{f}_1$ becomes negative
2. Both $f_{1}and{f}_2$ become negative
3. $f_1=f_2<f$
4. $f_1>fand{f}_2$ becomes negative

Q.

The graph between the lateral magnification (m) produced by a lens and the distance of the image (v) is given by

[MP PMT 1994]

1. 
2. 
3. 
4. 

Q. The ratio to radii of curvature of a biconvex lens $R_1:R_2$ = 2 : 3. Its refractive index and focal length is $1.5$ and $12cm$ respectively. What is the value of $R_1$? Consider $R_1$ and $R_2$ are positive and negative respectively.

1. $5cm$
2. $10cm$
3. $15cm$
4. $20cm$

Q. If ${\epsilon }_0$ and ${\mu }_0$ are the electric permittivity and magnetic permeability in a free space, $\epsilon$ and $\mu$ are the corresponding quantities in a medium, the index of refraction of the medium is,

1. $\sqrt{\frac{\epsilon }{{\epsilon }_0}}$
2. $\sqrt{\frac{{\epsilon }_0\mu }{\epsilon {\mu }_0}}$
3. $\sqrt{\frac{\epsilon \mu }{{\epsilon }_0{\mu }_0}}$
4. $\sqrt{\frac{{\epsilon }_0{\mu }_0}{\epsilon \mu }}$
   

Q. What should be the value of distance $d$ so that final image is formed on the object itself? (Focal lengths of the lenses are written on the lenses.)

1. $10cm$
2. $20cm$
3. $5cm$
4. None of these

Q. An object, a convex lens of focal length $20\text{cm}$ and a plane miror are arranged as shown in Fig. How far behind the mirror is the final image after reflection is formed?

1. $20\text{cm}$
2. $30\text{cm}$
3. $40\text{cm}$
4. $50\text{cm}$

Q. Calculate the smallest thickness of the soap bubble which produces a constructive interference for a red light of the wavelength $650\text{nm}$.

Take refractive index to be $1.33$.

1. $112.2\text{nm}$
2. $102.2\text{nm}$
3. $132.2\text{nm}$
4. $122.2\text{nm}$

Q. An object is placed at a distance of 40 cm from a thin converging lens of focal length 10 cm. The image distance is .

1. $\frac{50}{3}cm$
2. $\frac{40}{3}cm$
3. $\frac{60}{3}cm$
4. $\frac{20}{3}cm$

Q. Where should a convex lens of focal length $9cm$ be placed $\left(incm\right)$ between two point sources $S_1$ and $S_2$ which are $24cm$ apart, so that images of both the sources are formed at the same place? Find distance of lens from $S_1$ or $S_2$ whichever is lesser.

Q. Assertion $\left(\text{A}\right)$ : We cannot observe the diffraction pattern from a wide slit illuminated by monochromatic light.

Reason $\left(\text{R}\right)$ : In diffraction pattern all the bright bands are not of the same intensity.

1. Both $\text{A}$ and $\text{R}$ are true and $\text{R}$ is the correct explanation of $\text{A}$.
2. $\text{A}$ is true and $\text{R}$ is false.
3. $\text{A}$ is false and $\text{R}$ is true.
4. Both $\text{A}$ and $\text{R}$ are true and $\text{R}$ is not the correct explanation of $\text{A}$.

Q.

An object is plaved at a distance of 40 cm from a concave mirror of focal length 10 cm. What is the image distance for the given situation?

1. 10 cm

2. -10 cm

3. 8 cm

4. -8 cm

Q. A convex lens is in contact with a concave lens. The magnitude of the ratio of their focal lengths is $\frac{2}{3}$. Their equivalent focal length is 30cm. What are their individual focal lengths?

1. -15, 10
2. -10, 15
3. 75, 50
4. -75, 50

Q. A man with normal near point $25cm$ reads a book with small print using a magnifying glass, a thin convex lens of focal length $5cm$. The closest and farthest distances from the magnifying glass at which he can read the book when viewing through the magnifying glass, respectively are -

1. $4.17cm,5cm$
2. $3cm,6cm$
3. $2cm,3cm$
4. $5.17cm,6cm$

Q. A spherical surface of radius of curvature R separates air (refractive index 1.0) from glass (refractive index 1.5). The center of curvature is in the glass. A point object P placed in air is found to have a real image Q in the glass. The line PQ cuts the surface at a point Q, and PO = OQ. The distance PO is equal to

1. 5R
2. 3R
3. 2R
4. 1.5R

Q. A beam of unpolarized light is passed first through a tourmaline crystal $A$ and then through another tourmaline crystal $B$ , oriented so that its principal plane is parallel to that of $A$. The intensity of the emergent light is $I$. The crystal $A$ is now rotated by ${45}^{\circ }$ in a plane perpendicular to the direction of the incident ray. Find the ratio of the final intensity of the emergent light, in the second case, to that in the first case.

1. $\frac{1}{\sqrt{2}}$
2. $\frac{1}{4}$
3. $1$
4. $\frac{1}{2}$

Q. Assertion $\left(\text{A}\right)$ : We cannot observe the diffraction pattern from a wide slit illuminated by monochromatic light.

Reason $\left(\text{R}\right)$ : In diffraction pattern all the bright bands are not of the same intensity.

1. Both $\text{A}$ and $\text{R}$ are true and $\text{R}$ is the correct explanation of $\text{A}$.
2. Both $\text{A}$ and $\text{R}$ are true and $\text{R}$ is not the correct explanation of $\text{A}$.
3. $\text{A}$ is true and $\text{R}$ is false.
4. $\text{A}$ is false and $\text{R}$ is true.

Q. The ratio to radii of curvature of a biconvex lens $R_1:R_2$ = 2 : 3. Its refractive index and focal length is $1.5$ and $12cm$ respectively. What is the value of $R_1$? Consider $R_1$ and $R_2$ are positive and negative respectively.

1. $5cm$
2. $10cm$
3. $15cm$
4. $20cm$

Q. An object and its real image are located at distances $25\text{cm}$ and $40\text{cm}$ respectively from the two principal focii of a convex lens on either side. The linear magnification of the image is nearly equal to

1. $+1.3$
2. $-1.3$
3. $+1.8$
4. $-1.8$

Q. Two thin converging lenses are placed on a common axis, so that the center of one of them coincides with the focus of the other. An object is placed at a distance twice the focal length from the left-hand lens. Where will its image be? What is the lateral magnification? The focal length of each lens is $f$.

1. $0.25$
2. $-0.5$
3. $0.75$
4. $-1$