Chapter-10, Light - reflection and refraction

Explanation:

The principal focus of a concave mirror refers to the point on its principal axis where parallel rays of light incident on the mirror tend to converge after being reflected. It is a focal point that can be found halfway between the center of curvature and the vertex of the mirror. The symbol "F" represents the principal focus and its distance from the vertex of the mirror are represented by "f". The principal focus is a concept of importance in optics because it is used to determine the magnification and image formation in optical systems that make use of concave mirrors.

Explanation:

For a spherical mirror, the radius of curvature (R) and focal length (f) are related by the equation-

1/f = 2/R

Substituting R=20 cm in the above formula, we get-

1/f = 2/20 cm

Simplifying the right-hand side, we get:

1/f = 0.1 cm^-1

Taking the reciprocal of both sides, we get:

f = 10 cm

Hence, 10 cm is the focal length of the spherical mirror.

Explanation:

A concave mirror can give an erect and enlarged image of an object placed at a certain distance from the mirror. The distance of the object from the mirror and the focal length of the mirror determine the size and orientation of the image formed by the mirror. A concave mirror is also called a converging mirror because it converges light rays that fall on it.

Explanation:

We prefer convex mirrors as rear-view mirrors in vehicles because they provide a wider field of view than flat mirrors.

A convex mirror is curved outward, which means that it reflects light outwards and creates a smaller, more distorted image of the objects behind us. However, this distortion allows the mirror to reflect a wider field of view than a flat mirror, which only reflects a narrow area directly behind the vehicle.

This wider field of view allows the driver to see more of the surrounding area, which can be particularly useful when changing lanes or maneuvering in tight spaces. Additionally, the distorted image created by the convex mirror can make it easier to judge distances between objects, which can be especially helpful when parking or backing up.

In conclusion, the convex mirror provides a safer and more effective rear-view mirror for drivers, which is why it is preferred in vehicles.

Explanation:

For a convex mirror, the focal length (f) is half the radius of curvature (R). Therefore, in this case, the focal length is-

f = R/2 = 32 cm / 2 = 16 cm

So the focal length of the convex mirror is 16 cm.

Explanation:

We can use the mirror formula to solve this problem, which is-

1/f = 1/v + 1/u

where f is the focal length of the mirror, v is the distance of the image from the mirror, and u is the distance of the object from the mirror.

Since the mirror is concave and produces a real image, the focal length is negative. We are also given that the magnification of the image is 3, which means-

magnification = v/u = 3

Using these two equations, we can solve for v and u. Substituting v = 3u into the mirror formula, we get-

1/f = 1/3u + 1/u

Simplifying this equation, we get-

1/f = 4/3u

Multiplying both sides by u, we get-

u/f = 4/3

Substituting u = 10 cm, we get-

10/f = 4/3

Solving for f, we get-

f = -7.5 cm

So the focal length of the mirror is -7.5 cm. Now the magnification equation can be used to find the distance of the image from the mirror-

v/u = 3

v/10 = 3

v = 30 cm

Hence, the real image which is produced by the concave mirror is situated at a distance of 30 cm behind the mirror.

Explanation:

The light beam sways in the direction of normal.

A light beam is bent towards the normal when it moves from an optically rarer to an optically denser medium. Air is optically denser than water, hence a light ray traveling from the air would hit water and bends towards the average when it goes into the water.

Explanation:

Speed of light in vacuum divided by speed of light in medium gives the refractive index of a medium (nm).

The vacuum-bound speed of light (c) is 3 × 108 m/s.

Glass has a refractive index of 1.50 (ng).

Speed of light in glass (v) = Vacuum speed of light/Glass refractive index

= c/ng

=3 × 108/1.50 = 2x 108 ms-1.

Explanation:

Diamond has the highest optical density.

The most transparent substance is air.

A medium's refractive index and optical density are intimately correlated. The largest optical density will be found in a medium with the highest refractive index, and vice versa.

Table 10.3 shows that the refractive indices of air and diamond are the highest and lowest, respectively. As a result, the air has the lowest optical density while the diamond has the highest.

Explanation:

The relationship for a refractive index determines the speed of light in a given medium (nm). The relationship is provided as

From the relationship, it can be deduced that light moves the slowest through materials with high refractive indices and the fastest via those with low indices.

Table 10.3 shows that kerosene, turpentine, and water have corresponding refractive indices of 1.44, 1.47, and 1.33. Light moves through water the fastest, for this reason.

Explanation:

The relationship between a medium's refractive index (nm) and its light speed (v) is as follows:

c is the speed of light in a vacuum or in air.

Diamond has a refractive index of 2.42. This implies that compared to the speed of light in air, the speed of light in diamonds will be reduced by a ratio of 2.42.

Explanation:

P=1/F(in meters)

The reciprocal of a lens's focal length is referred to as the lens' power. The SI unit for lens power is the dioptre if P is the power of a lens with a focal length of fin metres. D stands for it.

The power of a lens with a 1-meter focal length is referred to as 1 dioptre.

1 D = 1 m−1

Explanation:

A convex lens's opposite side's center of curvature, 2F2, creates the image of an object placed in the center of curvature, 2F1, of the lens. As seen in the given illustration, the picture that forms is inverted and the same size as the object.

Since the image is true and the same size, it should be in position 2F.

It is assumed that the needle's image is produced 50 cm away from the convex lens. As a result, the needle is positioned 50 cm in front of the lens.

Distance to object (u) = -50 cm

50 cm is the image distance (v).

f = focal length

The formula for the lens states that

Explanation:

The concave lens's focal length is 2 metres.

Power of lens (P) = 1/f = 1/ (-2) = -0.5D

Due to the concave lens's divergent nature in this instance, a negative sign develops.

Hence, the supplied concave lens has a power of -0.5 D.

Explanation:

(d) A lens enables the passage of light through it. Clay lacks this quality, hence it can't be utilized to manufacture lenses.

A lens is a transparent piece of glass that, when light rays pass through it by refraction, concentrates or disperses the light.

Clay cannot be used to create lenses because it is an opaque substance that does not allow light to pass through.

Explanation:

The right response is (d). Between the pole of the mirror and its principal focus

Development of an image (virtual, erect, and larger than the object)

It is noted that a concave mirror produces the following image:

Concave mirrors can create virtual images, but only if something is positioned in front of the focal point.

Image formation: A concave mirror produces an erect image when an object is positioned between the concave mirror's pole and its focus.

Concave mirrors provide a magnified image that is only larger than the object when it is positioned between the mirror's pole and its main focus.

Conclusion→

Consequently, only when the object is positioned between the mirror's pole and its primary focus would the image created by a concave mirror be virtual, erect, and larger than the object.

Thus, choice (d) is the right one.

Explanation:

(b) An object's image is created at the center of curvature on the opposite side of a convex lens when it is put at the center of curvature in front of the lens. The resulting image is accurate, upside-down, and the same size as the original object.

Explanation:

(a) It is customary to interpret the focal length of a concave mirror and a concave lens as negative. As a result, the narrow spherical lens and the spherical mirror are both concave in shape.

Explanation:

(d) A convex mirror always projects a smaller, more erect, virtual version of the item in front of it. Similar to this, a plane mirror will always reflect an upright, virtual picture of the same size as the thing in front of it. As a result, the offered mirror could be convex or planar.

Explanation:

(c) When a convex lens is positioned between the radius of curvature and the focal length, it produces a magnified image of the object. Moreover, convex lenses with shorter focal lengths magnify more. Hence, a convex lens with a 5 cm focal length should be used for reading small print.

Explanation:

Object distance range: 0 to 15 cm

When an object is put between a concave mirror's pole (P) and the main focus, the picture is upright (F).

So, the object must be positioned anywhere between the pole and the focus of a concave mirror with a 15 cm focal length in order to produce an erect image of it. As seen in the above graphic, the image that is created will be virtual, erect, and magnified in nature.

Explanation: 

(a) Concave (b) Convex (c) Concave

(a) A car's headlights have concave mirrors. This is due to the fact that concave mirrors when the light source is positioned at their primary focus, can produce a strong parallel beam of light.

(b) A vehicle's side/rear view mirrors use convex mirrors. Convex mirrors to reflect the items in front of them in a virtual, elevated, and decreased form. They have a broad field of view as a result. It allows the motorist to view the majority of the traffic in front of them.

(c) Mirrors that are concave are convergent mirrors. They are utilised to build solar furnaces because of this.

The light that strikes concave mirrors converges at a single location known as the principle focus.

They can therefore be utilized to generate a lot of heat at that location.

Explanation:

Even if an object's half is covered with black paper, the convex lens will still create a complete image of the thing. It can be understood by using the next two examples.

Case I: Coverage of the upper half of the lens

In this scenario, the lower portion of the lens will bend a light ray originating from the item.

As seen in the following diagram, these rays collide on the other side of the lens to create the image of the target object.

Case II: When the lens's lower half is obscured

In this instance, the upper portion of the lens bends a light ray coming from the item. As seen in the following diagram, these rays collide on the other side of the lens to create the image of the target object.

Explanation:

The object's height is h0 = 5 cm.

Object's separation from converging lens, u = -25 cm

A converging lens's focal length is 10 cm.

By applying the lens formula,

As a result, the image is inverted, generated 16.7 cm behind the lens, and is 3.3 cm in size. Below is a diagram of the rays.

Explanation:

Concave lens's (OF1) f = - 15 cm focal length

Image separation, v=–10 cm

The formula for the lens states that

The item is 30 cm in front of the lens according to the negative value of u. The ray diagram that follows demonstrates this.

Explanation:

The Convex mirror's focal length (f) is +15 cm

Distance to object (u) = -10 cm

The mirror formula says that

On the opposite side of the mirror, the picture is situated 6 cm away from the mirror.

A plane mirror produces a +1 magnification. It demonstrates that the plane mirror's created image is the same size as the object. The affirmative signal demonstrates that the produced image is virtual and upright.

Explanation:

A plane mirror has a magnification of +1, meaning that the size of the image it creates is exactly equal to the size of the item that is generated behind the mirror.

The affirmative signal demonstrates that the produced image is virtual and upright.

Explanation:

Distance to object (u) = -20 cm

Height of object (h) = 5 cm

30 cm is the radius of curvature (R).

Focal length = 2 Radius of Curvature

R = 2f

f = 15 cm

The mirror formula says that

The picture formed is upright if the image height value is positive.

As a result, the image created is smaller, more synthetic, and more erect.

Explanation:

Distance to object (u) = – 27 cm

Height of object (h) = 7 cm

Focusing distance (f) = -18 cm

The mirror formula says that

The inverted nature of the image is indicated by a negative image height value.

Explanation:

A lens with a power of -2.0D has a focal length of -0.5m. The lens is concave.

The reciprocal of the lens's meter-long focal length is used to calculate its power (m).

Power of lens = 1/ focal length in meter.

Lens power (P) equals 1/f

P = -2D

f = -1/2 = -0.5 m

A concave lens has a negative focal length. As a result, it is a concave lens.

Explanation:

Lens power (P) equals 1/f

P = 1.5D

f = 1/1.5 = 10/15 = 0.66 m

The focal length of a convex lens is positive. It is a convex lens or a converging lens as a result.