A plano convex lens of refractive index $$\mu $$₁ and focal length ƒ₁ is kept in contact with another plano concave lens of refractive index $$\mu $$₂ and focal length ƒ₂. If the radius of curvature of their spherical faces is R each and ƒ₁ = 2ƒ₂, then $$\mu $$₁ and $$\mu $$₂ are related as -

A uniform metallic wire has a resistance of 18 $$\Omega $$ and is bent into an equilateral triangle. Then, the resistance between any two vertices of the triangle is -

A heat source at T = 10³ K is connected to another heat reservoir at T = 10² K by a copper slab which is 1 mthick. Given that the thermal conductivity of copper is 0.1 WK^–1m^–1, the energy flux through it in the steady state is -

If the magnetic field of a plane electromagnetic wave is given by (the speed of light = 3 × 10⁸ B = 100 × 10^–6 sin $$\left[ {2\pi \times 2 \times {{10}^{15}}\left( {t - {x \over c}} \right)} \right]$$ then the maximum electric field associated with it is -