A vessel of depth t is half filled with a liquid having refractive index n₁ and the other half is filled with water of having refractive index n₂. The apparent depth of the vessel as viewed from top is

• $\frac{2\mathrm{t} \left({\mathrm{n}}_1 + {\mathrm{n}}_2\right)}{{\mathrm{n}}_1 {\mathrm{n}}_2}$

• $\frac{\mathrm{t} {\mathrm{n}}_1 {\mathrm{n}}_2}{\left({\mathrm{n}}_1 + {\mathrm{n}}_2\right)}$

• $\frac{\mathrm{t} \left({\mathrm{n}}_1 + {\mathrm{n}}_2\right)}{2 {\mathrm{n}}_1 {\mathrm{n}}_2}$

• $\frac{{\mathrm{n}}_1 {\mathrm{n}}_2}{\left( {\mathrm{n}}_1 + {\mathrm{n}}_2 \right)}$

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^o with the x-axis meets the experimental curve at P. The coordinates of P will be

An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment distance are measured by 

Two lenses of power -15D and +5D are in contact with each other. The focal length of the combination is

The angle of incidence at which reflected light totally polarized for reflection from air to glass (refractive index n), is

If θ1 and θ2 be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip θ is given by

A beam of light from a source L is incident normally on a plane mirror fixed at a certain distance x from the source. The beam is reflected back as a spot on a scale placed just above the source L. When the mirror is rotated through a small angle θ, the spot of the light is found to move through a distance y on the scale. The angle θ is given by