A double convex lens, lens made of a material of refractive index , is placed inside two liquids or refractive indices and , as shown. . A wide, parallel beam of light is incident on the lens from the left. The lens will give rise to

The slab of a material of refractive index 2 shown in figure has curved surface APB of radius of curvature 10 cm and a plane surface CD. On the left of APB is air and on the right of CD is water with refractive indices as given in figure. An object O is placed at a distance of 15 cm from pole P as shown. The distance of the final image of O from P, as viewed from the left is

.A rod of glass ( = 1.5) and of square cross section is bent into the shape shown in the figure. A parallel beam of light falls on the plane flat surface A as shown in the figure. If d is the width of a side and R is the radius of circular arc then for what maximum value of light entering the glass slab through surface A emerges from the glass through B

An optical fibre consists of core of surrounded by a cladding of . A beam of light enters from air at an angle with axis of fibre. The highest for which ray can be travelled through fibre is

A prism having an apex angle and refraction index 1.5 is located in front of a vertical plane mirror as shown in figure. Through what total angle is the ray deviated after reflection from the mirror

In steel the young's modulus and the strain at the breaking point are  and 0.15 respectively the stress at the breaking point for steel is therefore

Hail stones fall from certain height If only 2% of the mass of the hail stone melt on reaching the ground,, the height from which they fall is ( g = 10 ms^-2, L = 80 cal/gm and J = 4.2J/cal)

=

A fish rising vertically up towards the surface of water with speed 3 observes a bird diving vertically down towards it with speed 9 . The actual velocity of bird is

The image of point P when viewed from top of the slabs will be

A cube of side 2 m is placed in front of a concave mirror focal length 1m with its face P at a distance of 3 m and face Q at a distance of 5 m from the mirror. The distance between the images of face P and Q and height of images of P and Q are

Two transparent slabs have the same thickness as shown. One is made of material A of refractive index 1.5. The other is made of two materials B and C with thickness in the ratio 1 : 2. The refractive index of C is 1.6. If a monochromatic parallel beam passing through the slabs has the same number of waves inside both, the refractive index of B is

We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 

If , then  by trapezoidal rule is

We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 

A wire of length L  and radius r is rigidly fixed at one end on stretching the other end of the wire a force F the increase in its lengths is L. If another wire of same material but of length 2 L and radius 2r, is stretched with a force of 2F, the increase in its length will he