Image in Thin Lens Using Formula

Q. A lens having focal length $f$ and aperture of diameter $d$ forms an image of intensity $I$. Aperture of diameter $\frac{d}{2}$ in central region of lens is covered by a black paper. Now Focal length of lens and intensity of image will be respectively

1. $f\text{and}\frac{I}{4}$
2. $\frac{3f}{4}\text{and}\frac{I}{2}$
3. $f\text{and}\frac{3I}{4}$
4. $\frac{f}{2}\text{and}\frac{I}{2}$

Q. Under what condition, a concave lens can make a real image?

1. Real object placed between optical centre $O$ and and focus $F_2$.
2. Virtual object placed between optical centre $O$ and focus $F_1$.
3. Real object placed at focus $F_2$.
4. Real object placed between $-\infty$ and $2F_2$.

Q. A point object $\text{O}$ is placed in front of a concave mirror of focal length $10\text{cm}$ as shown in the figure. A glass slab of refractive index $\mu =3/2$ and thickness $6\text{cm}$ is inserted between object and mirror. Find the position of final image when the distance between mirror and slab is $5\text{cm}$.

1. $17\text{cm}$ from the mirror
2. $15\text{cm}$ from the mirror
3. $16\text{cm}$ from the mirror
4. $12\text{cm}$ from the mirror

Q. The image for the converging beam after refraction through the curved surface is formed at:

1. $x=\frac{40}{3}\text{cm}$
2. $x=40cm$
3. $x=-\frac{40}{3}\text{cm}$
4. $x=\frac{180}{7}\text{cm}$

Q. A thin lens of focal length $f$ and its aperture diameter $d$, forms a real image of intensity $I$. Now the central part of the aperture of diameter $\left(\frac{d}{2}\right)$ is blocked by an opaque paper. The focal length and image intensity would change to

1. $f,\frac{I}{4}$
2. $\frac{3f}{4},\frac{I}{2}$
3. $f,\frac{3I}{4}$
4. $\frac{f}{2},\frac{I}{2}$

Q.

A parallel beam of light ray parallel to the x-axis is incident on a parabolic reflecting surface $x=2b{y}^2$ as shown in the figure. After reflecting it passes through the focal point $F$. What is the focal length of the reflecting surface?

Q. A central portion of width d = 0.5 mm is cut out of convex lens of focal length 10 cm. Both halves are tightly fitted against each other. A point object is placed at distance 15 cm from lens then

1. We get single real image of object
2. We get two real images of object
3. Distance of image/images from object is 45 cm
4. Separation between images is 1.5 mm

Q.

The diameter of the sun is $1.4\times {10}^9\text{m}$ and its distance from the earth is $1.5\times {10}^{11}\text{m}$. Find the radius of the image of the sun formed by a lens of focal length 20 cm.

Q. A point object is placed at $30\text{cm}$ from a convex glass lens $({\mu }_g=\frac{3}{2})$ of focal length $20\text{cm}$. The final image of the object will be formed at infinity, if

1. another concave lens of focal length $60\text{cm}$ is placed in contact with the previous lens.
   
2. another concave lens of focal length $30\text{cm}$ is placed in contact with the previous lens.
   
3. the whole system is immersed in a liquid of refractive index $\frac{4}{3}$.
   
4. the whole system is immersed in a liquid of refractive index $\frac{9}{8}$.
   
   

Q. In the given figure below, there are $2$ convex lenses $L_1$ and $L_2$ having focal length $f_1$ and $f_2$ respectively. The distance between $L_1$ and $L_2$ will be:

1. $f_1$
2. $f_2$
3. $f_1+f_2$
4. $f_1-f_2$

Q. A small air bubble is inside a transparent cube of side length $24\text{cm}$ and of refractive index $\frac{4}{3}$. If the apparent distance of air bubble when viewed from top of one of the faces is $9\text{cm}$, then its apparent distance when viewed from opposite face will be

1. $6\text{cm}$
2. $8\text{cm}$
3. $9\text{cm}$
4. $7\text{cm}$

Q. Consider a coaxial system of two thin convex lenses of focal length $f$ each separated by a distance $d$. The left column of the table below gives different possible conditions between $d$ and $f$, and the right column represents the nature of the lens combination. Choose the correct alternative.

$\text{Conditions}$	$\text{Nature}$
$\left(1\right)$ $d<f$	$\left(\text{P}\right)$ $\text{Convex}$
$\left(2\right)$ $d=2f$	$\left(\text{Q}\right)$ $\text{Plane glass slab}$
$\left(3\right)$ $d>2f$	$\left(\text{R}\right)$ $\text{Concave}$

1. $\text{1-P, 2-R, 3-Q}$
2. $\text{1-R, 2-P, 3-Q}$
   
3. $\text{1-P, 2-Q, 3-R}$
4. $\text{1-Q, 2-P, 3-R}$

Q. A point object $\text{O}$ is placed on the principal axis of a convex lens of focal length $10\text{cm}$ at $12\text{cm}$ from the lens. When object is displaced $1\text{mm}$ along the principal axis away from lens, magnitude of displacement of image is $x_1$ .When the lens is displaced by $1\text{mm}$ perpendicular to the principal axis, displacement of image is $x_2$ in magnitude. Find the value of $\left|\frac{x_1}{x_2}\right|$ upto 2 decimal places..

Q. The magnification of an object placed in front of a convex lens is +2. The focal length of the lens is 2 metres. Find the distance by which object has to be moved to obtain a magnification of -2 (in metres). ___

Q. A double convex lens made of material of refractive index $1.5$ & having radius of curvature of each surface of $10\text{cm}$ is immersed in a liquid of refractive index $3.0$. The lens will behave as:

1. converging lens of $f=10\text{cm}$
2. diverging lens of $f=10\text{cm}$
3. converging lens of $f=5\text{cm}$
4. diverging lens of $f=5\text{cm}$

Q. The rays of light incident at the spherical surface of the lens from two different directions as shown in the figure. The relation between focal length of the lens in two cases is:
($f_1$ and $f_2$ is focal length of lens for ray $1$ and $2$ respectively.)

1. $f_I>f_{II}$
2. $f_{II}>f_I$
3. $f_I=f_{II}$
4. Can't be compared

Q. An object $2.4\text{m}$ in front of a lens forms a sharp image on a film $12\text{cm}$ behind the lens. A glass plate $1\text{cm}$ thick, of refractive index $1.5$ is inserted between lens and film with its plane faces parallel to film. At what distance (from lens) should the object shifted to be in sharp focus of film?

1. $7.2\text{m}$
2. $2.4\text{m}$
3. $3.2\text{m}$
4. $5.6\text{m}$

Q. Two thin similar convex glass pieces are joined together front to front with its rear portion silvered such that a sharp image is formed $20\text{cm}$ from the mirror. When the air between the glass pieces is replaced by water $({\mu }_w=4/3)$, then the image formed from the mirror is at a distance of
[Assume, glass pieces have same refractive index as water]

1. $8\text{cm}$
2. $10\text{cm}$
3. $6\text{cm}$
4. $12\text{cm}$

Q. To construct a ray diagram, we use two light rays which are so chosen that it is easy to know their directions after reflection from the lens. List these two rays and state the path of these rays after refraction. Use these two rays to locate the image of an object placed between '$F$' and '$2F$' of a convex lens.

Q. A point object $\text{O}$ is placed on the principal axis of a convex lens of focal length $10\text{cm}$ at $12\text{cm}$ from the lens. When object is displaced $1\text{mm}$ along the principal axis away from lens, magnitude of displacement of image is $x_1$ .When the lens is displaced by $1\text{mm}$ perpendicular to the principal axis, displacement of image is $x_2$ in magnitude. Find the value of $\left|\frac{x_1}{x_2}\right|$ upto 2 decimal places..

Q. When a real object is placed $25\text{cm}$ from a lens, a real image is formed. Mark the wrong statement from the following:

1. The lens is a converging lens.
2. The image may be magnified or diminished.
3. The focal length of the lens is less than $25\text{cm}$.
4. The focal length of the lens may be greater than $25\text{cm}$.

Q. A converging becam of light forms a sharp image on a screen. A lens is placed in the path of the beam, at $10\text{cm}$ from the screen, it is found that the screen has to be moved $8\text{cm}$ further away from the lens to obtam a sharp image. The focal length and the nature of lens is.

1. $18.5\text{cm};\text{convex lens}$
2. $20.5\text{cm};\text{concave lens}$
3. $22.5\text{cm};\text{concave lens}$
4. $19.5\text{cm};\text{convex lens}$

Q. A thin lens of focal length $f$ and its aperture diameter $d$, forms a real image of intensity $I$. Now the central part of the aperture of diameter $\left(\frac{d}{2}\right)$ is blocked by an opaque paper. The focal length and image intensity would change to

1. $\frac{f}{2},\frac{I}{2}$
2. $f,\frac{I}{4}$
3. $\frac{3f}{4},\frac{I}{2}$
4. $f,\frac{3I}{4}$

Q. When a real object is placed $25\text{cm}$ from a lens, a real image is formed. Mark the correct statement$($s$)$ from the following:

1. The lens is a converging lens.
2. The image may be magnified or diminished.
3. The focal length of the lens is less than $25\text{cm}$.
4. The focal length of the lens may be greater than $25\text{cm}$.

Q. Under what condition, a concave lens can make a real image?

1. Real object placed between optical centre $O$ and and focus $F_1$.
2. Virtual object placed between optical centre $O$ and focus $F_1$.
3. Real object placed at focus $F_1$.
4. Real object placed between $-\infty$ and $2F_1$.

Q.

Q. A candle flame of length $3\text{cm}$ is placed at a distance of $3\text{m}$ from a wall. How far from the wall must a concave mirror be placed in order that it may form an image of flame $9\text{cm}$ high on the wall?

1. $425\text{cm}$
2. $500\text{cm}$
3. $450\text{cm}$
4. $650\text{cm}$

Q. A plano-convex glass lens $({\mu }_g=3/2)$ of radius of curvature $R=20cm$ is placed at a distance ${}^{\prime }{a}^{\prime }$ from a concave lens of focal length $40cm$. What should be the distance ${}^{\prime }{b}^{\prime }$ of a point object $O$ from plano-convex lens so that the position of final image is independent of $a$?

1. $20cm$
2. $30cm$
3. $40cm$
4. $60cm$

Q.
A parallel beam of light is incident on lens mirror combination as shown in figure, then after reflection from mirror

1. x-cordinate where beam converges is $\frac{-5\sqrt{3}}{2}$ cm
2. y-cordinate where beam converges is 5 cm
3. Beam diverges after reflection from mirror
4. Beam converges after reflection from mirror

Q. In the figure shown radius of curvature of either surface of equi convex half lens is $40\text{cm}$ and refractive index $1.5$. Its one side is silvered. A plane mirror is also placed. A small object $O$ is placed such that there is no parallax between final image formed by lens and mirror. If transverse length of final image formed by silvered lens system is twice that formed by mirror. Choose the correct options:

1. $a=2.5\text{cm}$
2. $b=5\text{cm}$
3. Distance of image from object is $15\text{cm}$
4. Image formed by silvered lens system is virtual