## Friday, September 30, 2022

### Basic 10 | Body Fluids and Circulation | Topic 3: Double Circulation, Regulation of Cardiac activity, Disorders

BASIC LEVEL TOPIC-WISE ONLINE TEST SERIES

### Basic 10 | Body Fluids and Circulation | Topic 2: Circulatory Pathways, Heart, Cardiac Cycle, ECG

BASIC LEVEL TOPIC-WISE ONLINE TEST SERIES

### Basic 10 | Body Fluids and Circulation | Topic 1: Blood and Lymph

BASIC LEVEL TOPIC-WISE ONLINE TEST SERIES

# Image Formation by Lenses

Lenses form images by refracting light.

# The Refractive Index (n)

It is the ratio of the speeds of light in a pair of media.

# Refraction through a Rectangular Glass Slab

Fix a white paper on a drawing board and place a rectangular glass slab on its middle.

# 10. LIGHT – REFLECTION AND REFRACTION

REFRACTION OF LIGHT

Light seems to travel along straight-line paths in a transparent medium.

# Sign Convention for Reflection by Spherical Mirrors

New Cartesian Sign Convention:

In this convention, the pole (P) of the mirror is taken as the origin. The principal axis of the mirror is taken as the x-axis (X’X) of the coordinate system.

The New Cartesian Sign Convention for spherical mirrors

The conventions are as follows:

a) The object is always placed to the left of the mirror. i.e., light from the object falls on the mirror from the left-hand side.

b) All distances parallel to the principal axis are measured from the pole of the mirror.

c) All the distances measured to the right of the origin (along + x-axis) are taken as positive while those measured to the left of the origin (along – x-axis) are taken as negative.

d) Distances measured perpendicular to and above the principal axis (along + y-axis) are taken as positive.

e) Distances measured perpendicular to and below the principal axis (along – y-axis) are taken as negative.

Sign conventions are applied to obtain the mirror formula and solve related numerical problems.

# Mirror Formula and Magnification

In a spherical mirror, the distance of the object from its pole is called the object distance (u).

The distance of the image from the pole of the mirror is called the image distance (v).

The distance of the principal focus from the pole is called the focal length (f).

This formula is valid in all situations for all spherical mirrors for all positions of the object.

Magnification (m)

It is the enlargement of the image formed by a spherical mirror, relative to the size of the object.

It is the ratio of the height of the image (h′) to the height of the object (h).

Magnification is also related to the object distance (u) and image distance (v). It can be expressed as:

The height of the object is taken to be positive as the object is placed above the principal axis.

The height of the image is taken as positive for virtual images and negative for real images.

A negative sign in the value of the magnification indicates that the image is real. A positive sign indicates that the image is virtual.

Problem: A convex mirror used for rear-view on an automobile has a radius of curvature of 3.00 m. If a bus is located at 5.00 m from this mirror, find the position, nature and size of the image.

Solution

Radius of curvature, R = + 3.00 m

Object-distance, u = – 5.00 m
Image-distance, v= ?

Height of the image, h′= ?

Focal length, f = R/2 = + 300 m/2 = +1.50 m (as the principal focus of a convex mirror is behind the mirror)

The image is 1.15 m at the back of the mirror.

The image is virtual, erect & smaller by a factor of 0.23.

Problem: An object, 4.0 cm in size, is placed at 25.0 cm in front of a concave mirror of focal length 15.0 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Find the nature and the size of the image.

Solution

Object-size, h = + 4.0 cm

Object-distance, u = – 25.0 cm

Focal length, f = –15.0 cm

Image-distance, v= ?

Image-size, h′= ?

v = – 37.5 cm

The screen should be placed at 37.5 cm in front of the mirror. The image is real.

Height of the image, h′ = – 6.0 cm

The image is inverted and enlarged.

# Image Formation by Spherical Mirrors

Find out approximate focal length of a concave mirror.

Mark 3 parallel lines P, F & C on a table such that the distance between any two successive lines is equal to the focal length of the mirror.

Place a stand with concave mirror over the line P such that its pole lies over the line.

Keep a bright object (e.g. burning candle) at a position far beyond C. Place a paper screen and move it in front of the mirror to obtain a sharp bright image of the candle flame.

Repeat the activity by placing the candle (a) just beyond C, (b) at C, (c) between F & C, (d) at F and (e) b/w P & F.

Nature, position and size of the image formed by a concave mirror depends on the position of the object in relation to points P, F & C.

# Representation of Images Formed by Spherical Mirrors Using Ray Diagrams

In an extended object, each small portion acts like a point source. An infinite number of rays originate from each point. But it is easier to consider only two rays, for the clarity of the ray diagram and to know their directions after reflection.

The intersection of at least two reflected rays gives the position of image of the point object. Any two of the following rays can be considered to locate the image.

a)    A ray parallel to the principal axis. After reflection, it passes through the principal focus in a concave mirror or appear to diverge from principal focus in a convex mirror.

b)   A ray through the principal focus of a concave mirror or directed towards the principal focus of a convex mirror. After reflection, it emerges parallel to the principal axis.

c)  A ray through the centre of curvature of a concave mirror or directed in the direction of the centre of curvature of a convex mirror. Then it is reflected back along the same path because the incident rays fall on the mirror along the normal to the reflecting surface.

d) A ray incident obliquely to the principal axis, towards pole (P), on the concave mirror or a convex mirror. It is reflected obliquely.

In all these cases, the laws of reflection are followed. i.e., angle of reflection equals angle of incidence.

(a) Image formation by a Concave Mirror

Ray diagrams:

 Position of the object Position of the image Size of the image Nature of the image At infinity At focus F Highly diminished, point-sized Real & inverted Beyond C b/w F & C Diminished Real & inverted At C At C Same size Real & inverted b/w C & F Beyond C Enlarged Real & inverted At F At infinity Highly enlarged Real & inverted b/w P & F Behind the mirror Enlarged Virtual & erect

When the object is between F & P, image is not obtained on the screen. Here, virtual image can be seen in mirror.

Uses of concave mirrors

·   Used in torches, search-lights and vehicles headlights to get powerful parallel beams of light.

·   Used as shaving mirrors to see a larger image of the face.

·   Used by dentists to see large images of teeth of patients.

·   Large concave mirrors are used to concentrate sunlight to produce heat in solar furnaces.

(b) Image formation by a Convex Mirror

Show a pencil in the upright position in front of a convex mirror. Its image in the mirror is erect and diminished.

As the pencil is moved away from the mirror, the image becomes smaller and moves closer to the focus.

Two positions of the object to study the image formed by a convex mirror are shown below.

(a) Formation of image when the object is at infinity

(b) Formation of image when the object is at a finite distance from the mirror

 Position of the object Position of the image Size of the image Nature of the image At infinity At the focus F, behind the mirror Highly diminished, point-sized Virtual & erect Between infinity and the pole P b/w P & F, behind the mirror Diminished Virtual & erect

In plane mirrors and concave mirrors of any sizes, we cannot see a full-length image of a distant object. But it is possible in a convex mirror with wider field of view.

A convex mirror is fitted in a wall of Agra Fort facing Taj Mahal to observe the full image of Taj Mahal.

Uses of convex mirrors

Convex mirrors give an erect, diminished, virtual image. Also, they have a wider field of view as they are curved outwards. So, they are used as rear-view (wing) mirrors in vehicles. It enables the driver to see traffic behind him.