Common Rays in Thin Lenses

Q.

An angular magnification (magnifying power) of 30X is desired using an objective of focal length 1.25 cm and an eyepiece of focal length 5 cm. How will you set up the compound microscope?

Q. Optical axis of a thin equi-convex lens is the $x-$ axis. The co-ordinates of a point object and its image are $(-40\text{cm},1\text{cm})$ and $(50\text{cm},-2\text{cm})$ respectively. Pole of the lens is located at :

[Assume that the lens is constrained to move only on $x-$ axis]

1. $x+20\text{cm}$
2. $x=-30\text{cm}$
3. $x=-10\text{cm}$
4. Origin

Q.

An object of size 3.0 cm is placed 14 cm in front of a concave lens of focal length 21 cm. Describe the image produced by the lens. What happens if the object is moved further away from the lens?

Q. A virtual erect image by a diverging lens is represented by
($u,v,f$ are coordinates)

1. 
2. 
3. 
4. 

Q. In an experiment to determine the focal length of a lens, the following readings were taken u=20.1+-0.2 cm, v=50.1+-0.5 cm. The percentage error in focal length is nearly___?

Q. an object and a screen are fixed at a distance 50cm apart when a converging lens is placed at two positions A and B between the object and the screen the image of object is found on the screen if the distance between A and B is 10cm then the focal length of the lens is (1) 12 cm (2) 10 cm (3) 8 cm (4) 6 cm

Q. Two thin convex lenses of focal length $f_{1}and{f}_2$ are separated by a horizontal distance d (where $d<f_1,d<f_2$) and their centers are displaced by a vertical separation $\Delta$ as shown in figure.

Taking the origin of coordinates O at the center of the first lens, the x and y coordinates of the focal point of this lens system, for a parallel beam of rays coming from the left, are given by:

1. $x=\frac{f_1{f}_2}{f_1+f_2},y=\Delta$
2. $x=\frac{f_1(f_2+d)}{f_1+f_2-d},y=\frac{\Delta }{f_1+f_2}$
3. $x=\frac{f_1{f}_2+d(f_1-d)}{f_1+f_2-d},y=\frac{\Delta (f_1-d)}{f_1+f_2-d}$
4. $x=\frac{f_1{f}_2+d(f_1-d)}{f_1+f_2-d},y=\frac{\Delta (f_1-d)}{f_1+f_2-d}$

Q. 88.In an experiment to measure the focal length of an equiconvex lens following measurements were made |u|=0.30cm and |v| =0.60cm. The image form is real .The focal length of the lens within error limits is

Q. The ratio of height of image produced by concave lens to a height of object is 0.5.Assume focal length of the lens is 10 cm.find the distance of image from the lens

Q. an object and screen is fixed at a distance D apart a thin converging lens of focal length f is placed in two positions between them to get the image on screen if the gap between two positions is x and the magnification for two positions is m1 and m2 then (1) f = x / m1 - m2 (2) f = x / m1 + m2 (3) f = x ( m1 + m2 ) / m1m2 (4) f = x ( m1 - m2 ) / m1m2

Q. An object placed at a dis†an ce of 16 mcm from a convex lens produces an image of magnification m(m>1). If the object is moved towards the lens by 8cm then again an image of magnification m is obtained. The numerical value of the focal length of the lens is (a)12cm (b)14cm (c)18cm (d)20cm

Q. For a concave lens of focal length $f$, the relation between object and image distances $u$ and $y$, respectively, from its pole can best be represented by($u=v$ is the reference line):

1. 
2. 
3. 
4. 

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

Q. A compound microscope has two convex lens system with focal lengths 2 cm and 5 cm. An object is 2.5 cm away from the objective lens. The tube length of microscope when magnification is maximum is equal to: (a) 18.2 cm (b) 14.2 cm (c) 8.2 cm (d) 4.2 cm

Q. A convex lens of focal length, $f=1.5\text{m}$ is placed in a system of coordinate axes such that its optical centre is at origin $\text{O}$ and principal axis coincides with the $\text{x-axis}$. An object$\left(S\right)$ and a plane mirror are arranged as shown in the figure. Find value of $d$ $\left(\text{in m}\right)$ so that $\text{y-coordinate}$ of the image (after refraction and reflection) is $0.3\text{m}$.
(Assume that $\tan \theta =0.3)$

1. $4\text{m}$
2. $3\text{m}$
3. $5\text{m}$
4. $6\text{m}$

Q. If an object is placed at $A(OA>f)$; where $f$ is the local length of the lens, the image is formed at $B$. A perpendicular is erected at $O$ and $C$ is choosen on it such that the $\angle BCA$ is a right angle. Then the value of $f$ will be:

1. $\frac{AB}{O{C}^2}$
2. $\frac{\left(AC\right)\left(BC\right)}{OC}$
3. $\frac{O{C}^2}{AB}$
4. $\frac{\left(OC\right)\left(AB\right)}{AC+BC}$

Q. show analytically from the lens equation that when the object is at the principal focus , the image is formed at infinity

Q. The angle made by the moon on an astronomical telescope is $0.1\text{rad}$. Focal length of the objective lens and the eyepiece of the telescope are $10\text{cm}$ and $5\text{cm}$ respectively. Find the angle subtended by the final image at the eyepiece, in case of the least strain on the eye.

1. $0.1\text{rad}$
2. $0.2\text{rad}$
3. $0.4\text{rad}$
4. $0.5\text{rad}$

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

Q. A concave lens forms the image of an object such that the dis†an ce between the object and image is 10cm. If magnification of the image is 1/4. The focal length of the lens is (1) 6cm (2) 20/3 cm (3) 10/7 cm (4) 40/9 cm.

Q. Under what condition a convex lens when placed in a medium acts as a ordinary glass plate?

Q.

(a) Determine the ‘effective focal length’ of the combination of the two lenses in Exercise 9.10, if they are placed 8.0 cm apart with their principal axes coincident. Does the answer depend on which side of the combination a beam of parallel light is incident? Is the notion of effective focal length of this system useful at all?

(b) An object 1.5 cm in size is placed on the side of the convex lens in the arrangement (a) above. The distance between the object and the convex lens is 40 cm. Determine the magnification produced by the two-lens system, and the size of the image.

Q. 20.Where should an object be placed from an converging lens of focal length 20cm, so as to obtain a real image of magnification 2?

Q. In displacement method, the distance between object and screen is $96\text{cm}$. The ratio of length of two images formed by a convex lens placed between them is $4.84$. Then choose the correct option(s).

1. The ratio of the length of object to the length of shorter image is $11/5$.
2. The distance between the two positions of the lens is $36\text{cm}$.
3. The focal length of the lens is $22.5\text{cm}$.
4. The distance of the lens from the shorter image is $30\text{cm}$.

Q. 76. In the displacement method using a convex lens we obtained two images corresponding to a seperation d of the lens . One image is magnified as much as the other is diminished . If m is the magnification of one image , find focal length of lens

Q. A concave lens has focal length 15 cm. At what distance should the object from the lens be placed so that it forms an image at 10 cm from the lens? Also find the magnification produced by the lens.

Q. The camera lens has an aperture of f and the exposure time is (1/60)s. What will be the new exposure time if the aperture become 1.4 f ?

1. $\frac{1}{46}$
2. $\frac{1}{56}$
3. $\frac{1}{72}$
4. $\frac{1}{31}$

Q. Lenses refract light to form images : a .......... lens can from both real and virtual images, but a diverging lens forms only ......... images.

Q. In which of the following phenomena, the heat waves travel along straight lines with the speed of light?

1. Thermal conduction
2. Natural convection
3. Thermal radiation
4. Forced convection

Q.

(a) At what distance should the lens be held from the figure in

Exercise 9.29 in order to view the squares distinctly with the maximum possible magnifying power?

(b) What is the magnification in this case?

(c) Is the magnification equal to the magnifying power in this case?

Explain.