Lens Formula

Q. RAYS FROM THE SUN ARE FOCUSSED BY A LENS OF DIAMETER 5 cm ON A BLOCK OF ICE AND 10 g OF ICE IS MELTED N 20 MIN . FIND THE HEAT FROM THE SUN REACHING THE EARTH PER MIN PER SQUARE cm ?

Q.

An object is first placed at $24cm$ from the lens and then at a distance of $16cm$ from the lens. If the magnification of the image formed in both the cases is same, determine the focal length of the lens.

Q. A plano convex lens of refractive index $1.5$ and radius of curvature $30\text{cm}$ is silvered at the curved surface. Now this lens has been used to form the image of an object. At what distance from this lens, an object needs to be placed in order to have a same size image of the object?

Q. If the distances of an object and its virtual image from the focus of a convex lens of focal length f are 1 cm each, then f is

1. $4cm$
2. $(\sqrt{2}+1)cm$
3. $2\sqrt{2}cm$
4. $(2+\sqrt{2})cm$

Q. A concave mirror of focal length $2\text{cm}$ is placed on a glass slab as shown in the figure. The image of point object $O$ formed due to reflection at mirror and then refraction by the slab

1. is virtual and on the object itself
2. is real and on the object itself
3. is virtual and on the pole of mirror
4. is virtual and at $2\text{cm}$ from pole of the concave mirror.

Q.

A convex lens of focal length f is placed somewhere in between an object and a screen. The distance between the object and the screen is x. If the numerical value of the magnification produced by the lens is m, then the focal length of the 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. 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. 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. A source of light is located from a convergent lens of focal length f=30 cm at a distance double the focal length of the convergent laws. At what distance from the lens should a flat mirror be placed so that the rays reflected from the mirror are parallel after passing through the lens for the second time. (in cm)

1. 10 cm
2. 25 cm
3. 45 cm
4. 60 cm

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. Find the focal length of the lens shown in figure. The radius of curvature is $R=10\text{cm}$ and the refractive index of material of the lens is $\frac{3}{2}$.

1. $+20\text{cm}$
2. $-30\text{cm}$
3. $-15\text{cm}$
4. $+10\text{cm}$

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. $-1$

Q.
$\mu =\frac{3}{2}$

Figure shows on object O at a distance of 40 cm from lens, a glass slab at 20 cm from lens. A concave mirror is to be placed such that final image after reflection is formed at object itself. What is/are separation of object from mirror?

1. 100 cm or 40 cm
2. 60 cm or 40 cm
3. 102 cm or 82 cm
4. 208 cm or 86 cm

Q. A candle placed 25 cm from a lens, forms an image on a screen placed 75 cm on the other end of the lens. The focal length and type of the lens should be

1. + 18.75 cm and convex lens
2. - 18.75 cm and concave lens
3. + 20.25 cm and convex lens
4. - 20.25 cm and concave lens

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

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

Q. The object distance u, the image distance v and the magnification m in a lens follow certain linear relations. These are

1. $\frac{1}{u}$ versus $\frac{1}{v}$
2. m versus u
3. u versus v
4. m versus $\frac{1}{u}$

Q. A convex lens of focal length f is placed somewhere in between an object and a screen. The distance between the object and the screen is x. If the numerical value of the magnification produced by the lens is m, then the focal length of the 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. Object is placed at a distance of 75cm from a screen . where should a convex lens of focal length 12 cm be placed so as to obtain real image of object

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.

the magnification prodeuced by a convex lens is 2 .write its value in both si unit and cgs unit

Q. Two point light sources are 24 cm apart. Where should a convex lens of focal length 9 cm be put in between them from one source so that the images of both the sources are formed at the same place

1. 6 cm
2. 9 cm
3. 12 cm
4. 15 cm

Q. Two point light sources are 24 cm apart. Where should a convex lens of focal length 9 cm be put in between them from one source so that the images of both the sources are formed at the same place

1. 6 cm
2. 9 cm
3. 12 cm
4. 15 cm