A Converging lens has a focal length of 10 cm in air. It is made of a material of refractive index 1.6. If it is immersed in a liquid of refractive index 1.3, find its new focal length. 

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Calculate the new focal length of a converging lens, initially with a focal length of 10 cm in air, when submerged in a liquid with a refractive index of 1.3.

A Converging lens has a focal length of 10 cm in air. It is made of a material of refractive index 1.6. If it is immersed in a liquid of refractive index 1.3, find its new focal length.

The new focal length is 26 cm

• Focal length of the lens in air, f = 10 cm
• Refractive index of the lens material, n = 1.6
• Refractive index of the surrounding medium (liquid), n_lq = 1.3

Using the formula provided:

1/f’ = ((n/n_lq) – 1) * (1/f)

Substituting the given values:

1/f’ = ((1.6/1.3) – 1) * (1/10) 1/f’ = ((8/13) – 1) * (1/10) 1/f’ = ((8/13) – (13/13)) * (1/10) 1/f’ = (-5/13) * (1/10) 1/f’ = -1/26

Therefore, the new focal length f’ is:

f’ = -26 cm

The negative sign indicates that the new focal length is on the opposite side of the lens from the side facing the object, which is consistent with the converging lens behavior. So indeed, the new focal length is 26 cm.

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Refelection of light by spherical mirrors

Reflection of light by spherical mirrors involves two types of mirrors: concave and convex. Here’s a brief overview of how light behaves when it reflects off these mirrors:

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1. Concave Mirrors:

   • A concave mirror is curved inward like the inside of a spoon.
   • When parallel rays of light strike a concave mirror, they converge or come together at a single point called the focal point (F).
   • The distance between the focal point and the mirror’s surface is called the focal length (f).
   • If an object is placed beyond the focal point, the reflected rays converge to form a real inverted image between the focal point and the mirror’s surface.
   • If the object is placed between the focal point and the mirror, the reflected rays diverge, and the image formed is virtual, erect, and larger than the object.

2. Convex Mirrors:

   • A convex mirror is curved outward like the back of a spoon.
   • When parallel rays of light strike a convex mirror, they diverge or spread apart.
   • The focal point for a convex mirror lies behind the mirror on the same side as the incoming light.
   • The image formed by a convex mirror is always virtual, upright, and smaller than the object.
   • It appears to be formed behind the mirror, but it’s not a real image.

The reflection of light by spherical mirrors obeys the laws of reflection:

• The angle of incidence is equal to the angle of reflection.
• Incident ray, reflected ray, and the normal to the surface at the point of incidence all lie in the same plane.

These principles govern how light interacts with spherical mirrors, leading to the formation of images that can be real or virtual, inverted or upright, and magnified or diminished depending on the position of the object relative to the mirror and its focal point.

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Categories: Math