^{st}January 2008 and 3rd January 2008. You can access all posts related to geometric optics by clicking on the

Today we will discuss a few more multiple choice practice questions in this section:

(1) The sun subtends an angle *θ* radian on the surface of the earth. If a convex lens of focal length *F* is used to obtain a real image of the sun on a screen, the diameter of the image will be

(a) *Fθ*

(b) *Fθ/*2

(c)* F/θ*

(d) 2*Fθ*

(e) impossible to be calculated with the given data.

Data is certainly sufficient for calculation. A very simple figure showing the formation of the image of the sun is shown. Since the sun is far away from the lens, its real image is formed at the focus of the lens. The angle subtended by this image at the optic centre of the lens is *θ* radian so that the diameter d of the image is *Fθ*.

[The sun subtends an angle of nearly 0.5º on the surface of the earth. If you use a convex lens of focal length 1 m, the diameter of the image will be *Fθ* = 1×(0.5×π/180), remembering that 180º = π radian. The diameter of the image will be nearly 0.0087 m = 0.87 cm].

(2) A slide projector gives a linear magnification of 20. If it projects a 4 cm×3 cm slide, the area of the image will be

(a) 0.24 m^{2}

(b) 0.48 m^{2}

(c) 4.8 m^{2}

(d) 24 m^{2}

(e) 48 m^{2}^{}

The length as well as the breadth will be magnified 20 times. In other words, the areal magnification is 20×20 = 400. Since the area of the slide is 12 cm^{2}, the area of the image will be 12×400 = 4800 cm^{2} = 0.48 m^{2}.

(3) Crown glass has refractive index 1.5. A cube of side 12 cm made of crown glass has a small air bubble inside and it appears to be at a distance of 6 cm when viewed normally through one face of the cube. If the air bubble is viewed normally through the opposite face, it will appear to be at a distance of

(a) 6 cm

(b) 5 cm

(c) 4 cm

(d) 3 cm

(e) 2 cm

In the case of *normal *refraction, the real distance *d*_{real} is related to the apparent distance *d*_{app} by the equation

* n = d*_{real }/*d*_{app}* *where *n* is the refractive *n* is with respect to the medium from which the object is viewed.

Therefore we have

1.5 = *d*_{real }/6 from which *d*_{real} = 9 cm.

Since the real distance of the air bubble from one face is 9 cm, the real distance from the opposite face_{ }is (12–9) cm = 3 cm.

Therefore the apparent distance *x *from the opposite face is given by

1.5 = 3/*x* from which *x = *2 cm [Option (e)].

(4) A thin plano-convex lens has focal length 40 cm. The radius of curvature of its curved surface is 20 cm. If its curved surface is silvered, it can function as a concave mirror of focal length very nearly

(a) 6.67 cm

(b) 8.48 cm

(c) 10 cm

(d) 20 cm

(e) 32.8 cm

When light is incident on the plane face, it is refracted by the plano-convex lens. Then it is reflected by the concave mirror formed by the silvered curved face. While returning, once again it is refracted by the plano-convex lens. In effect the system behaves as the combination of two

1/*F* = 1/*f*_{1 }+ 1/*f*_{2 }+ 1/*f*_{3} where *F* is the combined focal length and *f*_{1}, *f*_{2} and *f*_{3} are the

In the present case, *f*_{1} = *f*_{2 }= 40 cm and *f*_{3} = 10 cm.

Therefore, 1/*F* = 1/40 + 1/40 + 1/10 = 1/20 + 1/10 = 3/20

This gives *F* = 6.67 cm, nearly.

[If the above lens is silvered on its plane face instead of the curved face, the focal length *F* of the equivalent concave mirror will be given by

1/*F* = 1/40 + 1/40 + 1/∞ since the focal length of a plane mirror is infinity.

Therefore, *F* = 20 cm].