The image of a candle flame placed at a distance of 30 cm from a mirror is formed on a screen placed in front of the mirror at a distance of 60 cm from its pole. What is the nature of the mirror?

The image of a candle flame placed at a distance of 30 cm from a mirror is formed on a screen placed in front of the mirror at a distance of 60 cm from its pole. What is the nature of the mirror? Find its focal length. If the height of the flame is 2.4 cm, Find the height of its image. State whether the image formed is erect or inverted.

Based on the given information, we can determine the following:

Nature of the mirror:

The image formed on the screen is real because it is located on the other side of the mirror and can be viewed on a screen. Only concave mirrors can form real images. Therefore, the mirror in this scenario is concave.

Focal length:

We can use the mirror equation to find the focal length (f):

1/f = 1/u + 1/v

where:

• u = object distance (30 cm)
• v = image distance (60 cm)

Solving for f:

1/f = 1/30 + 1/60 f = (30 * 60) / (90) = 20 cm

Therefore, the focal length of the mirror is 20 cm.

Height of the image:

We can use the magnification formula to find the height of the image (h'):

m = h' / h = v / u

where:

• m = magnification
• h = object height (2.4 cm)

Since the image is real and formed on the opposite side of the mirror, the magnification is negative.

m = -60 / 30 = -2

Therefore, h' = m * h = -2 * 2.4 cm = -4.8 cm

However, the height of the image cannot be negative, so we interpret the negative sign as indicating the image is inverted.

Therefore, the image height is 4.8 cm and the image is inverted.

Summary:

• Mirror type: Concave
• Focal length: 20 cm
• Image height: 4.8 cm (inverted)

Reflection and Refraction

Reflection and refraction are fundamental phenomena in optics that describe how light interacts with surfaces and materials.

1. Reflection:

   • Reflection occurs when light bounces off a surface. The angle at which the light ray approaches the surface (incident angle) is equal to the angle at which it reflects off the surface (reflection angle), measured from the surface's normal (a line perpendicular to the surface).
   • There are two main types of reflection: specular reflection, which produces a clear and distinct image like a mirror, and diffuse reflection, which scatters light in various directions, resulting in a matte appearance.
   • Mirrors, polished metal surfaces, and still water are examples of surfaces that produce specular reflection, while rough surfaces such as paper or matte paints exhibit diffuse reflection.

2. Refraction:

   • Refraction occurs when light passes from one medium to another and changes direction due to a change in its speed. This change in direction is caused by the light's wavelength altering as it moves from one medium to another with a different optical density.
   • The change in direction depends on the angle of incidence and the refractive indices of the two materials. Snell's Law describes this relationship mathematically: n₁sin(θ₁) = n₂sin(θ₂), where n₁ and n₂ are the refractive indices of the two materials, and θ₁ and θ₂ are the angles of incidence and refraction respectively, measured from the normal.
   • Common examples of refraction include the bending of light as it passes through water or glass, the dispersion of light into its component colors by a prism, and the apparent bending of objects when seen through a transparent medium such as air or water.
   • Lenses, like those found in eyeglasses or cameras, use refraction to bend light in specific ways to produce images.

Both reflection and refraction play essential roles in various optical devices and natural phenomena, influencing how we perceive the world around us and enabling the functioning of technologies such as mirrors, lenses, and fiber optics.