The diameter of the aperture of a plano-convex lens is 6 cm and its maximum thickness is 3 mm. If the velocity of light in the material of the lens is 2 x 10⁸ m/s, its focal length is (approximately):

(1) 10 cm

(2) 15 cm

(3) 30 cm

(4) 60 cm

Two plano-convex lenses of equal focal lengths are arranged as shown.

The ratio of the combined focal lengths is:

(1) 1: 2: 1

(2) 1: 2: 3

(3) 1: 1: 1

(4) 2: 1: 2

When an object is at a distance of u₁ and u₂ from a lens, a real image and a virtual image is formed respectively having the same magnification. The focal length of the lens is:

(1) $u_1-u_2$

(2) $\frac{u_1-u_2}{2}$

(3) $\frac{u_1+u_2}{2}$

(4) $u_1+u_2$

A concave lens of focal length f produces an image (1/x) of the size of the object. The distance of the object from the lens is:

(1) (x - 1)f

(2) (x + 1)f

(3) {(x - 1)/x}f

(4) {(x + 1)/x}f

A thin equiconvex glass lens of refractive index 1.5 has a power of 5D. When the lens is immersed in a liquid of refractive index $\mathrm{\mu }$, it acts as a divergent lens of focal length 100 cm. The value of $\mathrm{\mu }$ of liquid is:

(1) 4 / 3

(2) 3 / 4

(3) 5 / 3

(4) 8 / 3

In the case of the displacement method of lenses, the product of magnification in both cases is:

(1) 1

(2) 2

(3) Zero

(4) Infinite

In the displacement method, a convex lens is placed in between an object and a screen. If the magnifications in the two positions are m₁ and m₂ and the displacement of the lens between the two positions is x, then the focal length of the lens is:

(1) $\frac{x}{m_1+m_2}$

(2) $\frac{x}{m_1-m_2}$

(3) $\frac{x}{{\left(m_1+m_2\right)}^2}$

(4) $\frac{x}{{\left(m_1-m_2\right)}^2}$

The focal length of a planoconvex glass lens is 20 cm $\left({\mu }_0=1.5\right)$. The plane face of it is silvered. An illuminating object is placed at a distance of 60 cm from the lens on its axis along the convex side. Then the distance (in cm) of the image is:

(1) 20

(2) 30

(3) 40

(4) 12

Two thin similar convex glass surfaces are joined together front to front with its rear portion silvered such that a sharp image of an object at infinity is formed 20 cm from the mirror. When the air between the glass pieces is replaced by water $\left({\mathrm{\mu }}_{\mathrm{w}}=4/3\right)$, then the image formed from the mirror is at a distance of: (Thickness of lens is negligible.)

(1) 8 cm

(2) 10 cm

(3) 6 cm

(4) 12 cm

A convex lens of focal length 100 cm and a concave lens of focal length 10 cm are placed coaxially at a separation of 90 cm. If a parallel beam of light is incident on the convex lens, then after passing through the two lenses, the beam:

(1) Converges

(2) Diverges

(3) Remains parallel

(4) Disappears