Lens Formula

Q.

Write lens formula and magnification.

Q. Q.1059 A concave mirror of focal length f1 is placed at a distance d from a convex lens of focal length f2. A beam of light coming from infinity and falling on this convex lens-concave mirror combination returms to infinity. The distance d must equal:

Q. The focal lengths of the objective and the eyepiece of a compound microscope are 2.0 cm and 3.0 cm respectively. The distance between the objective and the eyepiece is 15.0 cm. The final image formed by the eyepiece is at infinity. The two lenses are thin. The distance, in cm, of the object and the image produced by the objective, measured from the objective lens, are respectively

1. 2.4 and 15.0
2. 2.0 and 12.0
3. 2.0 and 3.0
4. 2.4 and 12.0

Q. Magnification of a compound microscope is $30$. Focal length of eyepiece is $5\text{cm}$ and the final image is formed at the least distance of distinct vision. Find the magnification of objective lens.

1. $5$
2. $7$
3. $9$
4. $3$

Q. A plano-convex lens is made of material of refractive index $1.6$. The radius of curvature of the curved surface is $60\text{cm}$. The focal length of the lens is

[Assume, surrounding medium to be air]

1. $200\text{cm}$
2. $100\text{cm}$
3. $50\text{cm}$
4. $400\text{cm}$

Q. The magnifications produced by a convex lens for two different positions of an object are m1 and m2 respectively (m1>m2). If d is the distance of separation between the two positions of the object then the focal length of the lens is? 1)m1m2 2)d/m1-m2 3)d12/m1-m2 4)d/m1-m2

Q.

The image of a small electric bulb fixed on the wall of a room is to be obtained on the opposite wall 3 m away by means of a large convex lens. What is the maximum possible focal length of the lens required for the purpose?

Q. An astronomical telescope has an angular magnification of magnitude of $5$ for distant objects. The length of a telescope is $36\text{cm.}$ The focal lengths of its objective and eye piece can be-

1. $30\text{cm};6\text{cm}$
2. $6\text{cm};30\text{cm}$
3. $60\text{cm};12\text{cm}$
4. $12\text{cm};60\text{cm}$

Q. When the real object is at distances $u_1$ and $u_2$, the images formed by the same lens are real and virtual respectively, and of the same size. Then the focal length of the lens is

1. $\frac{1}{2}\sqrt{u_1{u}_2}$
2. $\frac{1}{2}(u_1+u_2)$
3. $\sqrt{u_1{u}_2}$
4. $2(u_1+u_2)$

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. A convex lens of focal length f is placed some where in between an object and a screen. The distance between object and screen is x. if numerical value of magnification produced by lens is m, focal length of lens is:

1. $\frac{mx}{(m+1{)}^2}$
   
2. $\frac{mx}{(m-1{)}^2}$
   
3. $\frac{(m+1{)}^2}{m}x$
   
4. $\frac{(m-1{)}^2}{m}x$

Q. Curved surfaces of a plano-convex lens of refractive index \(\mu_1\) and a plano-concave lens of refractive index \(\mu _2\) have equal radius of curvatures as shown in figure. Find the ratio of radius of curvature to the focal length of the combined lenses.

Q.

Consider a concave mirror and a convex lens (refractive index = 1.5) of focal length 10 cm each, separated by a distance of 50 cm in air (refractive index = 1) as shown in the figure. An object is placed at a distance of 15 cm from the mirror. Its erect image formed by this combination has magnification $M_1$. When the set-up is kept in a medium of refractive index 7/6, the magnification becomes $M_2$. The magnitude $\left|\frac{M_2}{M_1}\right|$ is (give answer upto two decimal place)

Q. A card sheet divided into squares each of size 1 mm2 is being viewed at a distance of 9 cm through a magnifying glass (a converging lens of focal length 9 cm) held close to the eye. (a) What is the magnification produced by the lens? How much is the area of each square in the virtual image? (b) What is the angular magnification (magnifying power) of the lens? (c) Is the magnification in (a) equal to the magnifying power in (b)? Explain.

Q.

A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12 cm from P. At what point does the beam converge if the lens is (a) a convex lens of focal length 20 cm, and (b) a concave lens of focal length 16 cm?

Q. What happens to the intensity of light from a bulb if the distance from the bulb is doubled? As a laser beam travels across the length of a room, its intensity essentially remains constant.
What geometrical characteristic of LASER beam is responsible for the constant intensity which is missing in the case of light from the bulb?

Q. A linear object AB is at a distance of 36 cm from an equi convex lens of focal length 30 cm. In front of lens there is a plane mirror which is inclined at an angle ${45}^{\circ }$ with the principal axis of the lens at a distance l = 1 m from the mirror as shown in figure. A container with water layer d = 20 cm is placed as shown in the figure. Then choose the CORRECT statement(s). Take the refractive index of water as $\frac{4}{3}$

1. After reflection from the mirror the image of AB will be parallel to principal axis of the lens.
2. After reflection from the mirror the image of AB will be perpendicular to principal axis of the lens.
3. The value of H for which the sharp image of AB can be obtained at the bottom of the container is 80 cm

4. The value of H for which the sharp image of AB can be obtained at the bottom of the container is 85 cm.

Q. A convex lens (of focal length $20\text{cm}$) and a concave mirror, having their principal axes along the same lines, are kept $80\text{cm}$ apart from each other. The concave mirror is to the right of the convex lens. When an object is kept at a distance of $30\text{cm}$ to the left of the convex lens, its image remains at the same position even if the concave mirror is removed. The maximum distance of the object for which this concave mirror, would produce a virtual image by itself, would be:

1. $25\text{cm}$
2. $30\text{cm}$
3. $10\text{cm}$
4. $20\text{cm}$

Q. The length of a Galilean telescope is $33\text{cm}$ when focused to form an image at infinity. If the objective lens has a focal length of $35\text{cm}$, what is the focal length of the eyepiece?

1. $68\text{cm}$
2. $4\text{cm}$
3. $8\text{cm}$
4. $2\text{cm}$

Q. A convex lens of focal length $20\text{cm}$ is placed in front of a convex mirror with principal axis coinciding each other. The distance between the lens and mirror is $10\text{cm}$. A point object is placed on principal axis at a distance of $60\text{cm}$ from the convex lens. The image formed by combination, coincides the object itself. The focal length of the convex mirror is $\text{cm}$.

Q. The optical density of turpentine is higher than that of water while its mass density is lower. In the given figure it shows a layer of turpentine floating over water in a container. For which one of the four rays incident on turpentine in the path shown is correct?

1. 4
2. 3
3. 2
4. 1

Q.

A 5.0 diopter lens forms a virtual image which is 4 times the object placed perpendicularly on the principal axis of the lens. Find the distance of the object from the lens.

Q.

Linear magnification produced by a convex lens can be:

1. Less than 1 or more than 1

2. Less than 1 or equal to 1

3. More than 1 or equal to 1

4. Less than 1, equal to 1 or more than 1

Q. If a symmetrical bi-concave thin lens is cut into two identical halves, and they are placed in different arrangements as shown, then

1. Three images will be formed in case $\left(i\right)$
2. Two images will be formed in case $\left(ii\right)$
3. The ratio of focal lengths in $\left(ii\right)$ and $\left(iii\right)$ is $1$
4. The ratio of focal lengths in $\left(ii\right)$ and $\left(iii\right)$ is $2$

Q. An equi-convex lens of $\mu =1.5$ and $R=20\text{cm}$ is cut into two equal parts along its axis. Two parts are then separated by a distance of $120\text{cm}$ (as shown in figure). An object of height $3\text{mm}$ is placed at a distance of $30\text{cm}$ to the left of the first half lens. The final image will form at

1. $120\text{cm}$ to the right of first half lens, $3\text{mm}$ in size and inverted.
2. $150\text{cm}$ to the right of first half lens, $3\text{mm}$ in size and erect.
3. $150\text{cm}$ to the right of first half lens, $6\text{mm}$ in size and erect.
4. $120\text{cm}$ to the right of first half lens, $3\text{mm}$ in size and inverted

Q. For a given lens, the magnification was found to be twice as large as when the object was0.15 m distant from it as when the distance was 0.2 m. The focal length of the lens is (1) 1.5 m (2) 0.20 m(3) 0.10 m(4) 0.0 m

Q. A man with normal near point (25 cm) reads a book with small print using a magnifying glass: a thin convex lens of focal length 5 cm. (a) What is the closest and the farthest distance at which he should keep the lens from the page so that he can read the book when viewing through the magnifying glass? (b) What is the maximum and the minimum angular magnification (magnifying power) possible using the above simple microscope?

Q. If an object is placed asymmetrically between two plane mirrors, inclined at ${60}^{\circ }$, the total number of images formed is

1. infinite
2. 5
3. 4
4. 2

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

Q.

Consider a light beam incident from air to a glass slab at Brewster’s angle as shown in figure. A polaroid is placed in the path of the emergent ray at point P and rotated about an axis passing through the centre and perpendicular to the plane of the polaroid.

1. For a particular orientation there shall be darkness as observed through the polaroid.

2. The intensity of light as seen through the polaroid shall go through a minimum for four orientations of the polaroid.

3. The intensity of light as seen through the Polaroid shall go through a minimum but not zero for two orientations of the polaroid.

4. The intensity of light as seen through the polaroid shall be independent of the rotation