Cross-section view of a prism is the equilateral triangle ABC in the figure. The minimum deviation is observed using this prism when the angle of incidence is equal to the prism angle. The time taken by light to travel from P (midpoint of BC) to A is ______________ $$\times$$ 10^$$-$$10 s. (Given, speed of light in vacuum = 3 $$\times$$ 10⁸ m/s and cos30$$^\circ$$ = $${{\sqrt 3 } \over 2}$$)

An object is placed at a distance of 12 cm from a convex lens. A convex mirror of focal length 15 cm is placed on other side of lens at 8 cm as shown in the figure. Image of object coincides with the object.


When the convex mirror is removed, a real and inverted image is formed at a position. The distance of the image from the object will be .............. (cm)

A prism of refractive index n₁ and another prism of refractive index n₂ are stuck together (as shown in the figure). n₁ and n₂ depend on $$\lambda$$, the wavelength of light, according to the relation

$${n_1} = 1.2 + {{10.8 \times {{10}^{ - 14}}} \over {{\lambda ^2}}}$$ and $${n_2} = 1.45 + {{1.8 \times {{10}^{ - 14}}} \over {{\lambda ^2}}}$$

The wavelength for which rays incident at any angle on the interface BC pass through without bending at that interface will be _____________ nm.