In an experiment for estimating the value of focal length of converging mirror, image of an object placed at $$40 \mathrm{~cm}$$ from the pole of the mirror is formed at distance $$120 \mathrm{~cm}$$ from the pole of the mirror. These distances are measured with a modified scale in which there are 20 small divisions in $$1 \mathrm{~cm}$$. The value of error in measurement of focal length of the mirror is $$\frac{1}{\mathrm{~K}} \mathrm{~cm}$$. The value of $$\mathrm{K}$$ is __________.

In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass slab as 5.25 mm and apparent thickness of the glass slab as 5.00 mm. Travelling microscope has 20 divisions in one cm on main scale and 20 divisions on vernier scale is equal to 49 divisions on main scale. The estimated uncertainty in the measurement of refractive index of the slab is $$\frac{x}{10}\times10^{-3}$$, where $$x$$ is ___________

An object is placed on the principal axis of convex lens of focal length 10cm 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 5cm inside the mirror. The distance of the object from the lens is ___________ cm.

A ray of light is incident from air on a glass plate having thickness $$\sqrt3$$ cm and refractive index $$\sqrt2$$. 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 plate is ____________ $$\times$$ 10$$^{-2}$$ cm. (given $$\sin 15^\circ = 0.26$$)