(i)  A convex lens can form a magnified erect image when the object is placed between the optical centre and principal focus of the convex lens (i.e. between O and F).

(ii) A convex lens can form a magnified erect image when the object is placed between focus and the centre of curvature (i.e. between F' and 2F).

Object height, h = 4 cm; 
Object distance, u = -20 cm 
Nature of the lens = concave lens; 
Focal length = f = +10 cm 
Image distance, v = ? 
According to the lens formula,
\(\frac { 1 }{ f } =\frac { 1 }{ v } -\frac { 1 }{ u } \)
\(\Rightarrow \frac { 1 }{ v } =\frac { 1 }{ f } +\frac { 1 }{ u } \)
\(\frac { 1 }{ v } =\frac { 1 }{ +10 } +\frac { 1 }{ -20 } =\frac { 1 }{ 10 } -\frac { 1 }{ 20 } =\frac { 2-1 }{ 20 } =\frac { 1 }{ 20 } \)
∴ v=20cm
The image is formed at a distance of 20 cm from the lens on the opposite side.

(a)Laws of refraction of light states that the incident ray, the refracted ray and the normal at the point of incidence, all lie in the same plane.
(ii)The second law of refraction of light is the Snell's Law of Refraction. It state that the ratio of sine of angle of refraction is a constant for given pair of medium.
\({sin\ i\over sin\ r}\)=Constant (n)
This constant (n) is called refractive index of the medium.
(i)When the light is going from vacuum to another medium, then the value of refractive index is called the absolute refractive index.
(ii)The ratio of speed of light in vacuum to the speed of light in a medium is called the absolute refractive index of the medium, i.e.,
Absolute refractive index (of medium)=\(Speed\ of\ light\ in\ vacuum(C)\over Speed\ of\ light\ in\ medium(V)\)
(b)n_A=2.0;
n_B=1.5;
v_B=2 x 10⁸m/s
(i)Speed of light in vacuum, c=?
\(n_B=1.5={c\over v_B}\) 
c=n_B
v_B=1.5 x 2 x 10⁸ m/s
=3 x 10⁸ m/s
(ii)For medium 'A': n_A=\(c\over v_A\)
\(\therefore\ v_A={c\over n_B}={3\times10^8m/s\over2}\)
=1.5 x 10⁸ m/s

(b) Refractive index of glass from air
\(_{ a }{ { n }_{ g } }=\frac { 3 }{ 2 } \)
Refractive index of air from glass:
\(_{ g }{ { n }_{ a } }=\frac { 1 }{ _{ a }{ { n }_{ g } } } \)
\(\Rightarrow \frac { 1 }{ 3/2 } =\frac { 2 }{ 3 } \)

(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.

(i) A ray parallel to the principal axis and 
(ii) A ray passing through the centre of curvature of a concave mirror or appear to pass through the centre of curvature of convex mirror. 
Path of these rays after reflection is : 
(i) After reflection, the first ray will pass through the principal focus of a concave mirror or appear to diverge In case of a convex mirror. 
(ii) After reflection, the second ray is reflected back along the same path