Geometrical Optics — JEE Main PYQs

The critical angle for a denser-rarer interface is $45^{\circ }$. The speed of light in rarer medium is $3\times 10^8$ ms. The speed of light in the denser medium is:

The radius of curvature of each surface of a convex lens having refractive index 1.8 is 20 cm . The lens is now immersed in a liquid of refractive index 1.5. The ratio of power of lens in air to its power in the liquid will be $\mathrm{x}:1$. The value of x is ____ .

An ice cube has a bubble inside. When viewed from one side the apparent distance of the bubble is 12 cm. when viewed from the opposite side, the apparent distance of the bubble is observed as 4 cm. If the side of the ice cube is 24 cm, the refractive index of the ice cube is

Two convex lenses of focal length 20 cm each are placed coaxially with a separation of 60 cm between them. The image of the distant object formed by the combination is at ____ cm from the first lens.

A vessel of depth 'd' is half filled with oil of refractive index ${\mathrm{n}}_1$ and the other half is filled with water of refractive index $n_2$. The apparent depth of this vessel when viewed from above will be-

A fish rising vertically upward with a uniform velocity of $8{\mathrm{ms}}^{-1}$, observes that a bird is diving vertically downward towards the fish with the velocity of $12{\mathrm{ms}}^{-1}$. If the refractive index of water is $\frac{4}{3}$, then the actual velocity of …

A bi convex lens of focal length 10 cm is cut in two identical parts along a plane perpendicular to the principal axis. The power of each lens after cut is ______ D.

The refractive index of a transparent liquid filled in an equilateral hollow prism is $\sqrt{2}$. The angle of minimum deviation for the liquid will be ______°.

A monochromatic light wave with wavelength ${\lambda }_1$ and frequency $v_1$ in air enters another medium. If the angle of incidence and angle of refraction at the interface are $45^{\circ }$ and $30^{\circ }$ respectively, then the wavelength ${\lambda }_2$ and frequency $v_2$ …

A pole is vertically submerged in swimming pool, such that it gives a length of shadow 2.15 m within water when sunlight is incident at an angle of $30^{\circ }$ with the surface of water. If swimming pool is filled to a height of 1.5 m, then the height of the pole above the water s …

When one light ray is reflected from a plane mirror with $30^{\circ }$ angle of reflection, the angle of deviation of the ray after reflection is:

As shown in the figure, a plane mirror is fixed at a height of 50 cm from the bottom of tank containing water $\left(\mu =\frac{4}{3}\right)$. The height of water in the tank is 8 cm. A small bulb is placed at the bottom of the water tank. The distance of image of the bulb formed …

A thin cylindrical rod of length 10 cm is placed horizontally on the principle axis of a concave mirror of focal length 20 cm. The rod is placed in a such a way that mid point of the rod is at 40 cm from the pole of mirror. The length of the image formed by the mirror will be …

As shown in the figure, a combination of a thin plano concave lens and a thin plano convex lens is used to image an object placed at infinity. The radius of curvature of both the lenses is 30 cm and refraction index of the material for both the lenses is 1.75. Both the lenses are …

When a beam of white light is allowed to pass through convex lens parallel to principal axis, the different colours of light converge at different point on the principle axis after refraction. This is called :

A convex lens of refractive index 1.5 and focal length 18 cm in air is immersed in water. The change in focal length of the lens will be ______ cm.
(Given refractive index of water $=\frac{4}{3}$)

A ray of light is incident from air on a glass plate having thickness $\sqrt{3}\mathrm{cm}$ and refractive index $\sqrt{2}$. The angle of incidence of a ray is equal to the critical angle for glass-air interface. The lateral displacement of the ray when it passes through the pl …

The light rays from an object have been reflected towards an observer from a standard flat mirror, the image observed by the observer are :-
A. Real
B. Erect
C. Smaller in size then object
D. Laterally inverted

Choose the most appropriate answer from the options given below :

An object is placed on the principal axis of convex lens of focal length 10 cm as shown. A plane mirror is placed on the other side of lens at a distance of 20 cm . The image produced by the plane mirror is 5 cm inside the mirror. The distance of the object from the lens is …

A scientist is observing a bacteria through a compound microscope. For better analysis and to improve its resolving power he should. (Select the best option)

A thin prism ${\mathrm{P}}_1$ with an angle $6^{\circ }$ and made of glass of refractive index 1.54 is combined with another prism ${\mathrm{P}}_2$ made from glass of refractive index 1.72 to produce dispersion without average deviation. The angle of prism ${\mathrm{P}}_2$ …

A person has been using spectacles of power- 1.0 diopter for distant vision and a separate reading glass of power 2.0 diopters. What is the least distance of distinct vision for this person:

In an experiment for estimating the value of focal length of converging mirror, image of an object placed at 40 cm from the pole of the mirror is formed at distance 120 cm from the pole of the mirror. These distances are measured with a modified scale in which there are 20 small …

A microscope is focused on an object at the bottom of a bucket. If liquid with refractive index $\frac{5}{3}$ is poured inside the bucket, then microscope have to be raised by 30 cm to focus the object again. The height of the liquid in the bucket is:

Two objects A and B are placed at 15 cm and 25 cm from the pole in front of a concave mirror having radius of curvature 40 cm. The distance between images formed by the mirror is:

Light enters from air into a given medium at an angle of $45^{\circ }$ with interface of the air-medium surface. After refraction, the light ray is deviated through an angle of $15^{\circ }$ from its original direction. The refractive index of the medium is :

As shown in the figure, after passing through the medium 1. The speed of light $v_2$ in medium 2 will be :
$($ Given c $=3\times 10^8{\mathrm{ms}}^{-1})$

In normal adjustment, for a refracting telescope, the distance between objective and eye piece is 30 cm . The focal length of the objective, when the angular magnification of the telescope is 2 , will be:

The power of a lens (biconvex) is $1.25{\mathrm{m}}^{-1}$ in particular medium. Refractive index of the lens is 1.5 and radii of curvature are 20 cm and 40 cm respectively. The refractive index of surrounding medium :

An object 'O' is placed at a distance of 100 cm in front of a concave mirror of radius of curvature 200 cm as shown in the figure. The object starts moving towards the mirror at a speed 2 cm/s. The position of the image from the mirror after 10 s will be at ____ cm.

In an experiment with a convex lens, the plot of the image distance ($v^{\prime }$) against the object distance ($u^{\prime }$) measured from the focus gives a curve $v^{\prime }{u}^{\prime }=225$. If all the distances are measured in cm, the magnitude of the focal length of the lens is ____ cm.

A microscope was initially placed in air (refractive index 1). It is then immersed in oil (refractive index 2). For a light whose wavelength in air is $\lambda$, calculate the change of microscope's resolving power due to oil and choose the correct option

Which of the following statement is correct?

Time taken by light to travel in two different materials A and B of refractive indices ${\mu }_{\mathrm{A}}$ and ${\mu }_{\mathrm{B}}$ of same thickness is $t_1$ and $t_2$ respectively. If $t_2-t_1=5\times 10^{-10}s$ and the ratio of ${\mu }_A$ to ${\mu }_B$ is …

Light travels in two media ${\mathrm{M}}_1$ and ${\mathrm{M}}_2$ with speeds $1.5\times 10^8{\mathrm{ms}}^{-1}$ and $2.0\times 10^8{\mathrm{ms}}^{-1}$ respectively. The critical angle between them is:

In the given figure, the face AC of the equilateral prism is immersed in a liquid of refractive index 'n'. For incident angle $60^{\circ }$ at the side AC, the refracted light beam just grazes along face AC. The refractive index of the liquid $n=\frac{\sqrt{x}}{4}$. The value of …

A thin prism of angle $6^{\circ }$ and refractive index for yellow light (${\mathrm{n}}_{\mathrm{Y}}$) 1.5 is combined with another prism of angle $5^{\circ }$ and ${\mathrm{n}}_{\mathrm{Y}}=1.55$. The combination produces no dispersion. The net average deviation ($\delta$) produced by …

For an object placed at a distance 2.4 m from a lens, a sharp focused image is observed on a screen placed at a distance 12 cm from the lens. A glass plate of refractive index 1.5 and thickness 1 cm is introduced between lens and screen such that the glass plate plane faces paral …

A convex lens of focal length 20 cm is placed in front of convex mirror with principal axis coinciding each other. The distance between the lens and mirror is 10 cm. A point object is placed on principal axis at a distance of 60 cm from the convex lens. The image formed by combin …

The graph between $\frac{1}{u}$ and $\frac{1}{v}$ for a thin convex lens in order to determine its focal length is plotted as shown in the figure. The refractive index of length is 1.5 and its both the surfaces have same radius of curvatures R. The value of R will be ______ c …

A convex lens has power P. It is cut into two halves along its principal axis. Further one piece (out of the two halves) is cut into two halves perpendicular to the principal axis (as shown in figure). Choose the incorrect option for the reported pieces.

The refracting angle of a prism is A and refractive index of the material of the prism is $\cot (A/2)$. Then the angle of minimum deviation will be -

The speed of light in media 'A' and 'B' are $2.0\times 10^{10}\mathrm{cm}/\mathrm{s}$ and $1.5\times 10^{10}\mathrm{cm}/\mathrm{s}$ respectively. A ray of light enters from the medium B to A at an incident angle '$\theta$'. If the ray suffers total internal reflection, then

A small bulb is placed at the bottom of a tank containing water to a depth of $\sqrt{7}$ m. The refractive index of water is $\frac{4}{3}$. The area of the surface of water through which light from the bulb can emerge out is $x\pi$ m${}^2$. The value of x is ______.

A parallel beam of light is allowed to fall on a transparent spherical globe of diameter 30 cm and refractive index 1.5. The distance from the centre of the globe at which the beam of light can converge is ____ mm.

A light ray is incident, at an incident angle ${\theta }_1$, on the system of two plane mirrors ${\mathrm{M}}_1$ and ${\mathrm{M}}_2$ having an inclination angle $75^{\circ }$ between them (as shown in figure). After reflecting from mirror ${\mathrm{M}}_1$ it gets reflect …

Consider a light ray travelling in air is incident into a medium of refractive index $\sqrt{2n}$. The incident angle is twice that of refracting angle. Then, the angle of incidence will be :

The X-Y plane be taken as the boundary between two transparent media ${\text{M}}_1$ and ${\text{M}}_2$. ${\text{M}}_1$ in $Z\ge 0$ has a refractive index of $\sqrt{2}$ and ${\text{M}}_2$ with $Z<0$ has a refractive index of $\sqrt{3}$. A ray of light travelling in ${\text{M}}_1$ along th …

Two identical thin biconvex lenses of focal length 15 cm and refractive index 1.5 are in contact with each other. The space between the lenses is filled with a liquid of refractive index 1.25. The focal length of the combination is ______ cm.

A ray of ligh is incident at an angle of incidence $60^{\circ }$ on the glass slab of refractive index $\sqrt{3}$. After refraction, the light ray emerges out from other parallel faces and lateral shift between incident ray and emergent ray is $4\sqrt{3}\mathrm{cm}$. The thickn …