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

Yellow light is refracted through a prism producing minimum deviation. If i₁ and i₂ denote the angle of incidence and the angle of emergence for the prism respectively, then:

(1) i₁ = i₂

(2) i₁ > i₂

(3) i₁ < i₂

(4) i₁ + i₂ = 90

At what angle will a ray of light be incident on one face of an equilateral prism, so that the emergent ray may graze the second surface of the prism $(\mu =2)$?

(1) 30^o

(2) 90^o

(3) 45^o

(4) 60^o

A prism of the refractive index $\sqrt{2}$ has a refracting angle of 60^o. At what angle must a ray be incident on, so that it suffers a minimum deviation?

(1) 30^o

(2) 45^o

(3) 60^o

(4) 75^o

A glass prism of refractive index 1.5 is immersed in water of refractive index 4/3. A light ray incident normally on face AB is totally reflected at face AC if:

(1) $\sin \theta >8/9$

(2) $\sin \theta <2/3$

(3) $\sin \theta =\sqrt{3}/2$

(4) $2/3 < \sin \theta \le 8/9$

An astronomical telescope has an objective of focal length 100 cm and an eyepiece of focal length 5 cm. The final image of a star is seen 25 cm from the eyepiece. The magnifying power of the telescope is:

(1) 20

(2) 22

(3) 24

(4) 26