Lens Maker's Equation

An object is located $4 \mathrm{m}$ from the first of two thin converging lenses of focal lengths $2 \mathrm{m}$ and $1 \mathrm{m}$ respectively. The lenses are separated by $3 \mathrm{m}$. The final image formed by the second lens is located from the source at a distance of

Calculate the focal length of a reading glass of a person if his distance of distinct vision is $75$ $\mathrm{cm}$.

Graph of position of image vs position of point object from a convex lens is shown. Then, focal length of the lens is

A converging beam of rays is incident on a diverging lens. Having passed through the lens the rays intersect at a point $15 \mathrm{cm}$ from the lens on the opposite side. If the lens is removed the point where the rays meet will move $5 \mathrm{cm}$ closer to the lens. The focal length of the lens is

An equiconvex lens is cut into two halves along $\left(\mathrm{i}\right)$ $XOX\text{'}$ and $\left(\mathrm{ii}\right)$ $YOY\text{'}$as shown in the figure. Let $f, f^{\text{'}}, f^{\text{'}\text{'}}$ be the focal lengths of the complete lens, of each half in case $\left(\mathrm{i}\right)$, and of each half in case $\left(\mathrm{ii}\right)$, respectively.

Choose the correct statement from the following. 

The equiconvex lens has focal length $f$. If it is cut perpendicular to the principal axis passing through optical centre, then focal length of each half is

In an optics experiment, with the position of the object fixed, a student varies the position of a convex lens and for each position the screen is adjusted to get a clear image of the object. A graph between the object distance $u$ and the image distance $v,$ from the lens, is plotted using the same scale for the two axes. A straight line passing through the origin and making an angle of $45°$ with the $x$-axis meets the experimental curve at $P$. The coordinates of $P$ will be

A thin convex lens made from crown glass $\left(\mu =\frac{3}{2}\right)$ has focal $f$. When it is measured in two different liquids having refractive indices $\frac{4}{3}$ and $\frac{5}{3}$ it has the focal lengths $f_1$ and $f_2$ respectively. The correct relation between the focal lengths is

Two identical thin plano-convex glass lenses (refractive index $1.5$) each having radius of curvature of $20 \mathrm{cm}$ are placed with their convex surfaces in contact at the centre. The intervening space is filled with the oil of refractive index $1.7$. The focal length of the combination is

A plano-convex lens is made of material having refractive index $1.5.$ The radius of curvature of curved surface is $60 \mathrm{cm},$ The focal length of the lens is (in $\mathrm{cm}$)

In the figure, an air lens of radii of curvature $10 \mathrm{cm} \left(R_1=R_2=10 \mathrm{cm}\right)$ is cut in a cylinder of
glass $\left(\mu =1.5\right)$. The focal length and the nature of the lens is 

A double convex thin lens made of glass (refractive index $\mu =1.5$) has both radii of curvature of magnitude $20 \mathrm{cm}.$ Incident light rays parallel to the axis of the lens will converge at a distance $L$ such that

A convex lens of glass $\left(\mu =1.5\right)$ has a focal length of $8 \mathrm{cm}$ when placed in air. What is the focal length of lens when it is immersed in water $\left(\mu =\frac{4}{3}\right)?$

Convex lens made up of glass $\left({\mu }_{\mathrm{g}}=1.5\right)$ and radius of curvature $R$ is dipped into the water. Its focal length will be (Refractive index of water ${\mathit{\mu }}_w=\frac{4}{3}$) :

A convex lens (with material of refractive index of $\frac{3}{2}$) has two surfaces of equal radii of curvature $R$. The magnitude of its focal length is

Focal length of a convex lens is $20 \mathrm{cm}$ and its refractive index is $1.5$. It produces an erect, enlarged image if the distance from the object of the lens is

A candle placed $25 \mathrm{cm}$ from a lens forms an image on a screen placed $75 \mathrm{cm}$ on the other side of the lens. The focal length and type of the lens should be

The figure given below shows a beam of light-converging at point $P$. When a concave lens of the focal length $16 \mathrm{cm}$ is introduced in the path of the beam at a place $O$ shown by a dotted line such that $OP$ becomes the axis of the lens, the beam converges at a distance $x$ from the lens. The value $x$ will be equal to

The power of a thin convex lens $\left({}_a\mu _g=1.5\right)$ is $+5 \mathrm{D}$. When it is placed in a liquid of refractive index ${}_a\mu _l$ then it behaves as a concave lens of focal length $100 \mathrm{cm}$. The refractive index of liquid ${}_a\mu _l$ will be

An object is placed at a distance of $\frac{f}{2}$ from a convex lens of focal length $f$. The image will be