A point-like object is placed at a distance of $1m$ in front of a convex lens of focal length $0.5m$. A plane mirror is placed at a distance of $2m$ behind the lens. The position and nature of the final image formed by the system is 

A convex lens is put $10cm$ from a light source and it makes a sharp image on a screen, kept $10cm$ from the lens. Now a glass block (refractive index 1.5) of $1.5cm$ thickness is placed in contact with the light source. To get the sharp image again, the screen is shifted by a distance $d$. Then $d$ is :

The value of numerical aperature of the objective lens of a microscope is $1.25$. If light of wavelength $5000\mathring{A}$ is used, the minimum separation between two points, to be seen as distinct, will be :

A concave mirror has radius of curvature of $40cm$. It is at the bottom of a glass that has water filled up to $5cm$ (see figure). If a small particle is floating on the surface of water, its image as seen, from directly above the glass, is at a distance $d$ from the surface of water. The value of $d$ is close to : (Refractive index of water $=1.33$) 

A particle is oscillating on the X-axis with an amplitude $2cm$ about the point $x_0=10cm$ with a frequency $\omega$. A concave mirror of focal length $5cm$ is placed at the origin (see figure)
Identify the correct statements:
(A) The image executes periodic motion
(B) The image executes no n-periodic motion
(C) The turning points of the image are asymmetric w.r.t the image of the point at $x=10cm$
(D) The distance between the turning points of the oscillation of the image is $\frac{100}{21}$

A planoconvex lens becomes an optical system of $28cm$ focal length when its plane surface is silvered and illuminated from left to right as shown in Fig-A.
If the same lens is instead silvered on the curved surface and illuminated from other side as in Fig. B, it acts like an optical system of focal length $10cm$. The refractive index of the material of lens if:

A ray of light is incident at an angle of $60^{\circ }$ on one face of a prism of angle $30^{\circ }$. The emergent ray of light makes an angle of $30^{\circ }$ with incident ray. The angle made by the emergent ray with second face of prism will be:

Let the refractive index of a denser medium with respect to a rare medium be $N_{12}$ and its critical angle ${\theta }_C$ . At an angle of incidence A when light is travelling from denser medium to rarer medium, a part of the light is reflected and the rest is refracted and the angle between reflected and refracted rays is $90^o$. Angle A is given by :

In an experiment a convex lens of focal length $15cm$ is placed coaxially on an optical bench in front of a convex mirror at a distance of $5cm$ from it. It is found that an object and its image coincide, if the object is placed at a distance of $20cm$ from the lens. The focal length of the convex mirror is: 

A convex lens, of focal length $30cm$, a concave lens of focal length $120cm$, and a plane mirror are arranged as shown. For an object kept at a distance of $60cm$ from the convex lens, the final image, formed by the combination, is a real image, at a distance of :

To find the focal length of a convex mirror, a student records the following data:
The focal length of the convex lens is $f_1$ and that of mirror is $f_2$. Then taking index correction to be negligibly small, $f_1$ and $f_2$ are close to :

Two stars are 10 light years away from the earth. They are seen through a telescope of objective diameter 30 cm. The wavelength of light is 600 nm. To see the stars just resolved by the telescope, the minimum distance between them should be (1 light year $=9.46\times 10^{15}m$) of the order of:

To determine refractive index of glass slab using a travelling microscope, minimum number of readings required are:

If we need a magnification of $375$ from a compound microscope of tube length $150mm$ and an objective of focal length $5mm$, the focal length of the eye-piece, should be close to :

A large square container with thin transparent vertical walls and filled with water (refractive index $\frac{4}{3}$) is kept on a horizontal table. A student holds a thin straight wire vertically inside the water 12 cm from one of its corners, as shown schematically in the figure. Looking at the wire from this corner, another student sees two images of the wire, located symmetrically on each side of the line of sight as shown. The separation (in cm) between these images is _______.

A beaker of radius r is filled with water (refractive index $\frac{4}{3}$) up to a height H as shown in the figure on the left. The beaker is kept on a horizontal table rotating with angular speed $\omega$. This This makes the water surface curved so that the difference in the height of water level at the center and at the circumference of the beaker is $h(h<<H,h<<r)$, as shown in the figure on the right. Take this surface to be approximately spherical with a radius of curvature R. Which of the following is/are correct? (g is the acceleration due to gravity)

A thin convex lens is made of two materials with refractive indices $n_1$ and $n_2$, as shown in figure. The radius of curvature of the left and right spherical surfaces are equal. f is the focal length of the lens when $n_1=n_2=n$. The focal length is $f+\Delta f$ when $n_1=n$ and $n_2=n+\Delta n$. Assuming $\Delta n<<(n-1)$ and $(1<n<2)$, the correct statement(s) is/are?

A planar structure of length L and width W is made of two different optical media of refractive indices $n_1=1.5$ and $n_2=1.44$ as shown in figure. If $L>>W$, a ray entering from end AB will emerge from end CD only if the total internal reflection condition is met inside the structure. For $L=9.6$m, if the incident angle $\theta$ is varied, the maximum time taken by a ray to exit the plane CD is $t\times 10^{-9}$s, where t is _________. [Speed of light $c=3\times 10^8$ m/s]

Three glass cylinders of equal height $H=30cm$ and same refractive index $n=1.5$ are placed on a horizontal surface as shown in figure. Cylinder I has a flat top, cylinder II has a convex top and cylinder III has a concave top. The radii of curvature of the two curved tops are same (R = 3m ). If $H_1,H_2$ and $H_3$ are the apparent depths of a point X on the bottom of the three cylinders, respectively, the correct statement (s) is/are :

A monochromatic light is incident from air on a refracting surface of a prism of angle $75^o$ and refractive index $n_0=\sqrt{3}$. The other refracting surface of the prism is coated by a thin film of material of refractive index n as shown in figure. The light suffers total internal reflection at the coated prism surface for an incidence angle of $\theta \le 60^o$. The value of $n^2$ is ____ .

An optical bench has 1.5 m long scale having four equal divisions in each cm. While measuring the focal length of a convex lens, the lens is kept at 75 cm mark of the scale and the object pin is kept at 45 cm mark. The image of the object pin on the other side of the lens overlaps with image pin that is kept at 135 cm mark. In this experiment, the percentage error in the measurement of the focal length of the lens is ____ .

Sunlight of intensity $1.3kW{m}^{-2}$ is incident normally on a thin convex lens of focal length $20cm$. Ignore the energy loss of light due to the lens and assume that the lens aperture size is much smaller than its focal length. The average intensity of light, in $kW{m}^{-2}$, at a distance $22cm$ from the lens on the other side is _____.

For an isosceles prism of angle $A$ and refractive index $\mu$, it is found that the angle of minimum deviation ${\delta }_m=A$. Which of the following option(s) is/are correct? 

A monochromatic light is travelling in a medium of refractive index $n=1.6$. It enters a stack of glass layers from the bottom side at an angle $\theta =30^o$. The interfaces of the glass layers are parallel to each other. The refractive indices of different glass layers are monotonically decreasing as $n_m=n-m\Delta n$, where $n_m$ is the refractive index of the $m^{th}$ slab and $\Delta n=0.1$ (see the figure). The ray is refracted out parallel to the interface between the $(m-1{)}^{th}$ and $m^{th}$ slabs from the right side of the stack. What is the value of $m$? 

A parallel beam of light is incident from air at an angle $\alpha$ on the side PQ of a right-angled  triangular prism of refractive index $n=\sqrt{2}$. Light undergoes total internal reflection in the prism at the face PR when  $\alpha$ has minimum value of ${45}^{\circ }$. The angle $\theta$ of the prism is:

A plano-convex lens is made of a material of refractive index $n$. When a small object is placed $30$ cm away in front of the curved surface of the lens, an image of double the size of the object is produced. Due to reflection from the convex surface of the lens, another faint image is observed at a distance of $10$ cm away from the lens. Which of the following statement (s) is (are) true?

A transparent slab of thickness d has a refractive index n(z) that increases with z. Here z is the vertical  distance inside the slab, measured from the top. The slab is placed between two media with uniform refractive indices $n_1$ and $n_2$ $(>n_1)$, as shown in the figure. A ray of light incident with angle ${\theta }_i$ from medium 1 and emerges in medium 2 with refraction angle ${\theta }_f$ with lateral displacement $l$.
Which of the following statement(s) is (are) true?

A small object is placed $50cm$ to the left of a thin convex lens of focal length $30cm$ . A convex spherical mirror of radius of curvature $100cm$ is placed to the right of the lens at a distance of $50cm$. The mirror is titled such that the axis of the mirror is at a angle $\theta ={30}^{\circ }$ to the axis of the lens, as shown in the figure.
If the origin of the coordinate system is taken to be at the centre of the lens, the coordinates $(incm)$ of the point $(x,y)$ at which the image is formed are: