Image Formation by Lenses

Q. The maximum intensity in Young's double-slit experiment is $I_0$. Distance between the slits is $d=5\lambda$, where $\lambda$ is the wavelength of monochromatic light used in the experiment. What will be the intensity of light in front of one of the slits on a screen at a distance $D=10d$ ?

1. $\frac{I_0}{2}$
2. $\frac{3I_0}{4}$
3. $2I_0$
4. $\frac{I_0}{4}$

Q. The image of an object, formed by a plano-convex lens at a distance of 8 m behind the leens, is real is one third the size of the object. The wavelength of light inside the lens is $\frac{2}{3}$ times the wavelength in free space. The radius of the curved surface of the lens is

1. 1 m
2. 6 m
3. 3 m
4. 2 m

Q. In a single slit diffraction experiment, the width of the slit is doubled. The central maximum of the diffraction pattern will become,

1. narrower and fainter
2. narrower and brighter
3. broader and fainter
4. broader and brighter

Q. In Young's double- slit experiment, slits are separated by $0.5\text{mm}$ and the screen is placed $150\text{cm}$ away. A beam of light consisting of two wavelengths, $650\text{nm}$ and $520\text{nm}$, is used to obtain interference fringes on the screen. The least distance from the common central maximum to the point where the bright fringes due to both the wavelengths coincide are

1. $1.56\text{mm}$
2. $7.8\text{mm}$
3. $9.75\text{mm}$
4. $15.6\text{mm}$

Q. Sunlight of intensity $1.3kW{m}^{-2}$ is incident normally on a thin convex lens of focal length $20cm$. Ignore the energy loss of light due to the lens and assume that the lens aperture size is much smaller than its focal length. The average intensity of light (in $kW{m}^{-2}$), at a distance $22cm$ from the lens on the other side is

Q. In the Young's double slit experiment using a monochromatic light of wavelength $\lambda$, the path difference (in terms of an integer n) corresponding to any point having half the peak intensity is

1. $(2n+1)\frac{\lambda }{2}$
2. $(2n+1)\frac{\lambda }{8}$
3. $(2n+1)\frac{\lambda }{4}$
4. $(2n+1)\frac{\lambda }{16}$

Q. A double slit interference experiment is carried out in air and the entire arrangement is dipped in water. As a result

1. The fringe width decreases.
2. The fringe width increases.
3. The fringe width remains unchanged.
4. Fringe pattern disappears.

Q. Young's double slit experiment is carried out using microwaves of wavelength $\lambda =3\text{mm}.$ Distance between the slits is $d=5\text{mm}$ and the distance between the plane of slits and the screen is $D=100\text{cm}$. Find the total number of maxima formed on the screen.

1. $5$
2. $1$
3. $2$
4. $3$

Q. The graph of magnitude of object distance and magnitude of image distance for the various position of an object in front of a convex lens is shown in the figure.
The object distance & image distance is in $\text{cm}$, based on graph the focal length of lens is :

1. $20\text{cm}$
2. $40\text{cm}$
3. $10\text{cm}$
4. $30\text{cm}$

Q. A young's double slit experiment is conducted in the water $\left({\mu }_1\right)$ as shown in the figure. A glass plate of thickness $t$ and refractive index ${\mu }_2$ is placed on the path of $S_2$. Find the magnitude of optical path difference at $O$.

1. $\left|(\frac{{\mu }_2}{{\mu }_1}-1)t\right|$
   
2. $\left|(\frac{{\mu }_1}{{\mu }_2}-1)t\right|$
   
3. $\left|\right({\mu }_2-{\mu }_1\left)t\right|$
   
4. $\left|\right({\mu }_2-1\left)t\right|$
   

Q. In Young's double-slit experiment with slit separation $0.1\text{m}$, one observes a bright fringe at angle $1/40\text{rad}$ by using the light of wavelength ${\lambda }_1$. When the light of wavelength ${\lambda }_2$ is used a bright fringe is seen at the same angle in the same setup. Given that ${\lambda }_1$ and ${\lambda }_2$ are in the visible range $(380\text{nm}$ to $740\text{nm})$, their values are

1. $400\text{nm},500\text{nm}$
2. $625\text{nm},500\text{nm}$
3. $380\text{nm},525\text{nm}$
4. $380\text{nm},500\text{nm}$

Q. A thin lens of refractive index 1.5, and focal length in air of $20cm$ is placed inside a large container containing two immiscible liquids as shown below. If an object is placed at an infinite distance close to principle axis (common intersection of the two layers), then the distance between images is (in $cm$)

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

Q. Semiconductor is opaque for light of wavelength less than 800 nm and it is not opaque for light of wavelength greater than 800 nm. Energy gap of semiconductor in electron volt is [Take $hc=1240eV-nm$](Answer up to two decimal places)

Q.

Why diffraction occurs at wavelength comparable to the size of object? Why not we link diffraction with amplitude of wave?

Q. A double slit of separation $0.1\text{mm}$ is illuminated by white light. A coloured interference pattern is formed on a screen $100\text{cm}$ away. If a pinhole is located in this screen at a distance of $2\text{mm}$ from the central fringe, the wavelengths in the visible spectrum $\left(4000\dot{\text{A}}\text{to}7000\dot{\text{A}}\right)$ which will be absent in the light transmitted through the pinhole is

1. $4000\dot{\text{A}}$
2. $5000\dot{\text{A}}$
3. $6000\dot{\text{A}}$
4. $7000\dot{\text{A}}$

Q.

An enemy plane is at a distance$300km$ from the radar. In how much time, the radar will be able to detect the plane? (Take, the velocity of radio waves as $3\times {10}^{8}m{s}^{-1}$)

Q.

A convex lens of diameter 8.0 cm is used to focus a parallel bam of light of wavelength 620 nm. If the light be focused at a distance of 20 cm from the lens, what would be th eradius of the central bright spot formed?

Q. State the effect on the image in a pinhole camera if the luminous object is moved towards the pinhole.

Q. List - 1 gives different lens configurations. Radius of curvature of each surface is depicted in figure. Refractive index of glass of lens is $\frac{3}{2}$ and medium in which it is placed is 1. Rays of light parallel to axis of lens from left passes through lens and get focussed at distance x from lens. List - 2 gives value of x, then correct match is

1. $I\to P,II\to P,III\to R,IV\to R$
2. $I\to R,II\to R,III\to P,IV\to P$
3. $I\to P,II\to R,III\to P,IV\to R$
4. $I\to P,II\to S,III\to R,IV\to R$

Q. To remove myopia a lens of power 9.66D is reqiured. The dis†an t point of eye i

Q. State whether given statement is True or False
A virtual, erect and magnified image can be formed only by a convex lens.

1. True
2. False

Q. 27. If an object is at rest and placed in front of a mirror which is moving with speed v towards the object then what will be the speed of image ?

Q. The image of a star is formed by a convergent lens of focal length $1\text{m}$ and diameter $5\text{cm}.$ If the lens is ideal and the effective wavelength in image formation is taken as $5\times {10}^{-5}\text{cm},$ the diameter of the image formed will be nearest to

1. Zero
2. $2.5\times {10}^{-6}\text{cm}$
3. $2.5\times {10}^{-5}\text{cm}$
4. $2.5\times {10}^{-3}\text{cm}$

Q. Where should an object be placed so that a real and inverted image of same size is obtained using a convex lens?

1. Between the lens and its focus
2. At twice the focal length
3. At the focus
4. At infinity

Q. The maximum intensity in Young's double-slit experiment is $I_0$. Distance between the slits is $d=5\lambda$, where $\lambda$ is the wavelength of monochromatic light used in the experiment. The intensity of light in front of one of the slits on a screen at a distance $D=10d$ is $\frac{I_o}{m}$.
Find $m$

Q.

In a young’s double-slit experiment $\mathrm{d}=1\mathrm{mm}$ and $\mathrm{D}=200\mathrm{cm}$. It is found that the $9^{\mathrm{th}}$ bright fringe is at a distance of $6.5\mathrm{mm}$ from the $2^{\mathrm{nd}}$ dark fringe of the fringe pattern. What is the wavelength of light used?

1. $\frac{2500}{7}$

2. $\frac{5000}{7}$

3. $5000$

4. $433.33\mathrm{\AA }$

Q. Consider the diffraction pattern for a small pinhole. As the diameter of the hole is increased

1. The diameter of central bright spot decreases
2. The diameter of central bright spot increases
3. The intensity of the central bright spot increases
4. The intensity of the central bright spot decreases

Q. When an object is placed between F and 2F in front of a convex lens, the image formed is :

1. real and inverted
2. beyond 2F
3. magnified
4. all of these

Q. List - 1 gives different lens configurations. Radius of curvature of each surface is depicted in figure. Refractive index of glass of lens is $\frac{3}{2}$ and medium in which it is placed is 1.2 . Rays of light parallel to axis of lens from left passes through lens and get focused at distance x from lens. List - 2 gives value of x then correct match is.

1. $I\to Q,II\to Q,III\to T,IV\to T$
2. $I\to R,II\to R,III\to U,IV\to U$
3. $I\to Q,II\to Q,III\to S,IV\to S$
4. $I\to R,II\to R,III\to S,IV\to S$