Angle of refraction = 40^o 
Deviation of rays 
Angle of emergence = 55^o 
Direction of rays 

ㄥi = Angle of incidence 
ㄥr = Angle of refraction

(a) Image is of same size as the object.
(b) Image is virtual and erect.

The ray passing through the centre of curvature incident to the mirror along its normal so angle i = angle r = 0. Therefore, the ray retraces its path.

\(-\frac { v }{ u } =\frac { h' }{ h } \\ \frac { -v }{ -15 } =\frac { -1.5 }{ 1 } \\ v=-22.5cm\)

A lens of short focal length

Image is real

Between pole and principal focus

Between pole and focus, behind the convex mirror.

(i) When ray of light enters from air medium into water, medium it bends towards the normal as shown.

(ii) When ray of light enters from water medium into air medium, it bends away from the normal as shown

\(^{ g }{ n }_{ d }=1.6.{ n }_{ g }=1.5,{ n }_{ d }=?\\ ^{ g }{ n }_{ d }=\frac { { n }_{ d } }{ { n }_{ g } } \Rightarrow 1.6-\frac { { n }_{ d } }{ 1.5 } \\ or\quad { n }_{ d }=1.6\times 1.5=2.40\)

The focal length of a lens depends on
(a) Radii of curvature of the surface of the lens.
(b) Nature of material of the lens.
(c) Nature of medium in which lens is placed.

The field of view of a convex mirror is wider than that of concave mirror and convex mirror always produces erect image of object, so we prefer convex mirror as rear view mirror for vehicles.

The principal focus of a concave mirror is a point on the principal axis at which a light ray parallel to the principal axis converges after reflection.
Light rays that are parallel to the principal axis of a concave mirror converge at a specific point on its principal axis after reflecting from the mirror. This point is known as the principal focus of the concave mirror.
It is denoted by F.
 

(a) Sign conventions
1. The object is always placed to the left of the mirror.
2. All the distances parallel to the principal axis are always measured from the pole of the spherical mirror.
3. All the distances measured along the direction of incident light (along +ve x-axis), are considered to be positive.
4. Those distances measured opposite to the direction of incidence light (i.e. along -ve x-axis), are taken as negative.
5. The distances measured in upward direction, i.e. perpendicular to and above the principal axis (along +ve y-axis), are taken as positive.
6. The distances measured in the downward direction, (along -ve y-axis), i.e. perpendicular to and below the principal axis are taken as negative.
(b) u=-16cm, m=-3 for real But \(m=-\frac { v }{ u } =-3\)
v = 3u = 3 (-16) = -48 cm. 
Using mirror formula
\(\frac { 1 }{ f } =\frac { 1 }{ v } +\frac { 1 }{ u } \)
We get, \(\frac { 1 }{ f } =\frac { 1 }{ -48 } +\frac { 1 }{ -16 } \)
\(=\frac { 1 }{ -48 } -\frac { 1 }{ 16 } =\frac { -1-3 }{ 48 } =\frac { -4 }{ 48 } =\frac { -1 }{ 12 } \)
f=-12cm
(c) Negative sign of focal length indicated that mirror is concave in nature.

(b) CB=-uCF = -fCB=-v 
The relation between u, v and f is given by the lens formula:
\(\frac { 1 }{ f } =\frac { 1 }{ v } -\frac { 1 }{ u } \)
As both u and v are negative the above equation will change to
\(\frac { 1 }{ f } =\frac { 1 }{ (-v) } -\frac { 1 }{ (-u) } \)
\(\frac { 1 }{ f } =\frac { -1 }{ v } +\frac { 1 }{ u } \)
\(\Rightarrow \frac { 1 }{ f } =\frac { 1 }{ u } -\frac { 1 }{ v } \)
We know that the focal length of a concave lens is negative, so the above equation will be changed to
\(\frac { 1 }{ -f } =\frac { 1 }{ u } -\frac { 1 }{ v } \)
\(\Rightarrow \frac { 1 }{ f } =\frac { 1 }{ v } -\frac { 1 }{ u } \)
(c) Magnification m=-1 
v = + 40 cm (real and inverted) 
Nature of the lens = ? 
Power of the lens, P =?
\(\frac { v }{ u } =m\Rightarrow \frac { +40 }{ u } =-1\)
40=-u ⇒ u = -40 cm 
According to the lens formula,
\(\frac { 1 }{ f } =\frac { 1 }{ v } -\frac { 1 }{ u } \)
\(\Rightarrow \frac { 1 }{ f } =\frac { 1 }{ 40 } -\frac { 1 }{ -40 } =\frac { 1 }{ 40 } +\frac { 1 }{ 40 } =\frac { 2 }{ 40 } =\frac { 1 }{ 20 } \)
f = +20 cm 
fis +ve thus the lens is convex
\(P=\frac { 1 }{ f(metres) } =\frac { 1\times 100 }{ 20 } =+5D\)
Since power of lens is positive, lens will be converging in nature.

In a concave mirror an erect image will be obtained when the object is placed between pole and focus of the mirror.

Since, focal length is 12 cm, 
(i) Therefore, the range of object distance is between 0 cm to <12 cm (from zero to less than 12 cm). 
(ii) Image formed wall be magnified. i.e. larger than the object. 
(iii) If the object is placed at 24 cm in front of the mirror, it means that object is placed at 2F. ie., at the centre of curvature (at C) of the mirror.

The real, inverted and same size (of the object) image will also be formed at 24 cm.

(i) Yes.If a convex lens of focal length 10cm is covered one half with a black paper, it can produce an image of the complete object between F₂ and 2F₂.The rays of light coming from the object get refracted by the upper half of the lens. The image formed will be real, inverted and diminished.

(ii)Object height, h₁=4cm
Focal length, f=+20cm
Object distance, u=-15cm
Image distance, v=?
Image height, h₂=?
By lens formula,
\({1\over f}={1\over v}-{1\over u}\)
\(\Rightarrow\ {1\over v}={1\over f}+{1\over u}={1\over +20}+{1\over -15}={1\over 20}-{1\over 15}\)
\(\Rightarrow\ {1\over V}={3-4\over 60}={-1\over 60}\)
v=-60cm
Negative sign of v shows that the image is virtual.

Given m = -3, v = 80 cm, u = ?
Using the expression \(m=\frac { -v }{ u } \)
we have \(-3=\frac { 80 }{ u } \)  or \(u=\frac { -80 }{ 3 } =-26.67cm\)
The image is real and the lens is a convex lens.

The following are the laws of refraction of light.
(i)The incident ray, the refracted ray and the normal to the interface of two transparent media at the point of incidence, all lie in the same plane.
(ii)The ratio of sine of angle of incidence to the sine of angle of refraction is a constant, for the light of a given pair of media. This law is also known as Snell's law of refraction. The ray diagram is as shown. As seen in the refracted ray are in the same plane.