Light [Part: 4]

A concave mirror has a focal length of 10 cm. An object is placed 30 cm in front of the mirror. Where is the image formed?

• 15 cm

• 10 cm

• 20 cm

• 30 cm

Answer explanation

Using the mirror formula 1/f = 1/v + 1/u, where f = -10 cm (focal length for concave), u = -30 cm (object distance), we find v = 15 cm. Thus, the image is formed 15 cm in front of the mirror.

A convex lens forms an image 18 cm away from the lens when an object is placed 12 cm in front of it. What is the focal length of the lens?

• 6 cm

• 8 cm

• 9 cm

• 12 cm

Answer explanation

Using the lens formula 1/f = 1/v - 1/u, where v = 18 cm and u = -12 cm (object distance is negative), we find 1/f = 1/18 + 1/12. Solving gives f = 9 cm, confirming the correct answer is 9 cm.

A light ray in air enters a glass slab with a refractive index of 1.5. If the angle of incidence is 30°, what is the angle of refraction?

• 20°

• 15°

• 10°

• 25°

Answer explanation

Using Snell's Law, n1*sin(theta1) = n2*sin(theta2). Here, n1=1 (air), n2=1.5 (glass), theta1=30°. Thus, sin(theta2) = (1*sin(30°))/1.5 = 0.333. Therefore, theta2 = sin^(-1)(0.333) ≈ 20°. Hence, the angle of refraction is 20°.

A concave mirror produces an image that is 3 times the size of the object. If the object is placed 10 cm in front of the mirror, where is the image located?

• 30 cm

• 20 cm

• 10 cm

• 15 cm

Answer explanation

In a concave mirror, the magnification (M) is given by M = -image distance (v) / object distance (u). Here, M = 3 and u = -10 cm. Thus, 3 = -v / -10, leading to v = 30 cm. The image is located 30 cm in front of the mirror.

A convex lens has a power of +4D. What is the focal length of the lens?

• 0.25 m

• 0.5 m

• 0.4 m

• 0.2 m

Answer explanation

The power of a lens (P) is related to its focal length (f) by the formula P = 1/f. Given P = +4D, we can find f: f = 1/P = 1/4 = 0.25 m. Thus, the focal length of the lens is 0.25 m.

A concave lens has a focal length of -10 cm. An object is placed 20 cm from the lens. Where is the image formed?

• 5 cm

• 10 cm

• 15 cm

• 20 cm

Answer explanation

Using the lens formula 1/f = 1/v + 1/u, where f = -10 cm and u = -20 cm, we find 1/v = 1/f - 1/u = 1/(-10) - 1/(-20) = -1/10 + 1/20 = -1/20. Thus, v = -10 cm, indicating the image is formed 10 cm on the same side as the object.

A light ray enters from water (refractive index 1.33) into air. If the angle of incidence in water is 45°, what is the angle of refraction in air?

• 60°

• 30°

• 45°

• 50°

Answer explanation

Using Snell's Law, n1*sin(theta1) = n2*sin(theta2). Here, n1=1.33 (water), n2=1 (air), and theta1=45°. Solving gives sin(theta2) = 1.33*sin(45°)/1, leading to theta2 ≈ 60°. Thus, the angle of refraction in air is 60°.

A convex mirror has a focal length of 20 cm. An object is placed 40 cm from the mirror. Where is the image formed?

• 13 cm

• 20 cm

• 10 cm

• 15 cm

Answer explanation

Using the mirror formula 1/f = 1/v + 1/u, where f = -20 cm (focal length for convex), u = -40 cm (object distance), we find v = 13 cm. Thus, the image is formed 13 cm behind the mirror.

A concave lens forms an image 12 cm from the lens when an object is placed 24 cm in front of it. What is the focal length of the lens?

• 6 cm

• 8 cm

• 10 cm

• 12 cm

A convex lens forms a real image that is twice the size of the object. If the object is placed 15 cm from the lens, where is the image formed?

• 30 cm

• 25 cm

• 20 cm

• 35 cm