By going through these CBSE Class 12 Physics Notes Chapter 9 Ray Optics and Optical Instruments, students can recall all the concepts quickly.

## Ray Optics and Optical Instruments Notes Class 12 Physics Chapter 9

→ The image formed by a concave mirror cannot lie beyond the focus.

→ Real images are always inverted.

→ Virtual images are always erect.

→ The minimum distance between an object and its real image formed by a concave mirror is zero.

→ The angle of deviation on refraction of light from a plane surface is given by δ = |i – r|.

→ The absolute R.I. of any medium is always greater than one.

→ The frequency of light does not change during the refraction of light.

→ When light travels from rarer to denser medium its wavelength decreases as λ_{m} = \(\frac{\lambda}{\mu}\) and μ > 1, so λ_{m} < λ. where λ_{m} is the wavelength of light in the denser medium.

→ If the critical angle for water is C, then the fish just below the surface of the water can see in an angular range of 2C.

→ When i = r = 0, then refraction takes place without a change in the path of the ray of light.

→ The value of the refractive index depends on the following:

(a) Nature of the media of incidence and refraction.

(b) Temperature of media.

(c) Colour of light or wavelength of light.

→ ‘μ’ decreases with the increase in temperature.

→ μ is independent of the angle of incidence.

→ The transmission involves two refractions.

→ The maximum value of μ is for diamond (μ = 2.46).

→ The critical angle for the red rays is more than that for blue rays.

→ The critical angle increases with temperature.

→ Critical angle depends on the refractive index, the colour of light and temperature of the medium.

→ Air bubbles in glass appear silvery-white due to the total internal reflection from them.

→ Critical angles for water-air, glass-air and diamond-air are 45° 42° and 24° respectively.

→ The critical angle for ordinary glass is 42°

→ Thicker is the lens, more is the bending of light rays, thus lesser is its focal length and hence more is the power of the lens and vice-versa for a thin lens i.e., the thin lens has less power and longer focal length.

→ To produce dispersion without deviation, the angle of crown glass prism has to be greater than that of flint glass prism i.e., A > A’ and (μ’ – 1) > (μ’ – 1).

→ For no dispersion, the materials and the angles of the two prisms should be chosen so that their dispersive powers are in the inverse ratio of the deviations suffered by mean light through the prism. To produce deviation without dispersion, the angle of the crown glass prism has to be greater than that of the flint glass prism.

→ As μv, μr and μ are constant for a given material, so dispersive power (ω) of given material of a prism cannot be changed. But if glass material is chosen in such a way that μv is greater and μr is lower, then co can be higher.

→ A single lens cannot be free from chromatic aberration as it has different focal length for different colours and thus they are focused at different points.

→ To compare the size of the two objects, they should be placed at the least distance of distinct vision i.e. D = 25 cm.

→ The magnifying power of the simple microscope is small.

→ For greater magnification, a compound microscope is used which has net magnifying power as the product of linear magnifications or magnifying powers of each lens.

→ The image formed by the simple microscope is erect and magnified while the image formed by the compound microscope is inverted.

→ A simple microscope is also called a reading lens and is also used for repair of small instruments while compound microscope cannot be used for these purposes.

→ Magnifying power of an astronomical telescope is greater in case of the image formed at the least distance of distinct vision than in case of normal adjustment i.e, \(\frac{\mathrm{f}_{0}}{\mathrm{f}_{\mathrm{e}}}\)(1 + \(\frac{\mathrm{f}_{\mathrm{e}}}{\mathrm{D}}\)) > \(\frac{\mathrm{f}_{0}}{\mathrm{f}_{\mathrm{e}}}\)

→ The skin becomes visible before the actual sunrise and remains visible after actual sunset due to refraction. It increases the length of the day by nearly 4 minutes.

→ The image of an object when seen through a slab of thickness and R.I. μ is shifted by a distance, d = t(1 – \(\frac{1}{\mu}\))

→ When the object is in a denser medium, then its apparent depth is lesser than the actual depth if observed from the rarer medium.

→ When the object is in a rarer medium, then its apparent depth is greater than the actual depth if observed from the denser medium. The focal length of a lens immersed in water becomes four times the focal length in air.

→ Rainbow is seen only by a person with his back facing the sun and his eyes make an angle of 42° with the axis of the rainbow.

→ The nature of the lens does not change if it is placed in a rarer medium i.e.,μ_{g} > μ_{med} but the focal length in the medium becomes more than that in air i.e. f_{m} > f_{a}.

→ If μ_{m} > μ_{g} i.e. if it is placed in a denser medium, then the nature of the lens changes. Tire focal length may increase or decrease depending on the value of \(\frac{\mu_{g}-\mu_{m}}{\mu_{m}}\) as compared to (μ_{g} – 1).

→ f_{m} increases if \(\frac{\mu_{\mathrm{g}}-\mu_{\mathrm{m}}}{\mu_{\mathrm{m}}}\) > (μ_{g} – 1)

→ f_{m} decreases if \(\frac{\mu_{\mathrm{g}}-\mu_{\mathrm{m}}}{\mu_{\mathrm{m}}}\) < (μ_{g} – 1)

→ f_{m} = f_{a}, if \(\frac{\mu_{\mathrm{g}}-\mu_{\mathrm{m}}}{\mu_{\mathrm{m}}}\) = (μ_{g} – 1)

→ The lens becomes invisible if μ_{m} = μ_{g} and behaves as a plain glass with no refraction.

→ Amplitude, intensity, velocity and wavelength of the wave change on refraction.

→ In a denser medium, refraction does not occur when the angle of incidence is greater than the critical angle.

→ Rainbow is caused by the combined effect of refraction, total internal reflection and dispersion of sunlight by the raindrops suspended in the air.

→ Black is not the colour of light. It shows the absence of light.

→ White is also not the colour of light. It depicts the presence of all the colours.

→ Blue, green and red is primary colours.

→ Our eye is not sensitive to UV and infrared light.

→ Tire final image formed by the reflecting telescope is free from chromatic aberration. Also, the brightness of the image formed is higher.

→ The far point of the normal eye is at infinity.

→ Far Point: The farthest point up to which the eye can see clearly is called the far point.

→ Least distance of distinct vision: It is defined as the distance at which the eye can see the objects clearly. For a normal eye, it is 25 cm.

→ Small deviation produced by a prism is independent of the angle of incidence.

→ A pure spectrum is defined as that spectrum in which there is no missing constituent colour.

→ An impure spectrum is one in which there is overlapping of almost all the colours so at the centre of the spectrum we obtain a white spot with edges coloured with red and violet.

→ Transmission: It is defined as the passing of a ray of light through the medium.

→ Optical path: It is the product of the refractive index of the medium (μ) and the distance covered in it (n).

i. e., optical path = μ_{x} = μ (geometrical path).

→ For refraction from rarer to denser medium, r < i.

→ Critical angle: It is defined as the angle of the incidence in the denser medium for which the angle of refraction is 90° in the rarer medium.

→ Dispersion: It is defined as the process of splitting up white light into its constituent colours on passing through the prism.

→ Cauchy’s Formula: It states that the R.I. of a material depends on the wavelength (λ) as:

μ = a + \(\frac{b}{\lambda^{2}}+\frac{c}{\lambda^{4}}\)

→ Spectrum: It is defined as the band of colours that are obtained due to the dispersion of light.

→ Rainbow: Beautiful colours seen in the sky when the sun shines after the rain.

→ Fraunhofer lines: They are defined as the large number of dark lines observed in the spectrum of sunlight which corresponds to the absorption spectrum.

→ Primary rainbow: It is the rainbow in which the violet and red rays make angles 410 and 43° respectively with the axis of the rainbow. The red colour lies at the top while violet at the bottom.

→ Secondary rainbow: It is the rainbow in which the violet and red colours make angles 54° and 51° respectively with its axis. It is less bright than a primary rainbow. The violet colour lies on the outer edge while red on the inner edge.

→ The primary rainbow is formed due to two refractions and one total internal reflection of light incident on the droplet while the secondary rainbow is formed due to two refractions and two total

→ internal reflections of the light incident on the droplets.

→ Angular dispersion: It is defined as the difference between the angles of deviation for the extreme colours.

→ Dispersive power: It is defined as the ratio of angular dispersion to the mean deviation.

→ Chromatic aberration: It is defined as the process due to which a lens forms images of different colours at different distances from the lens.

→ Chromatic aberration = f_{r} – f_{v}.

**Important Formulae**

→ μ = \(\frac{C}{v}=\frac{\sin \mathrm{i}}{\sin \mathrm{r}}\),

where i = angle of incidence,

→ ^{a}μ_{w} = \(\frac{\text { Real depth }}{\text { apparent depth }}\)

→ μ =\(\frac{1}{\sin C}\) when C = critical angle

→ ^{w}μ_{g} = \(\frac{{ }^{a} \mu_{g}}{{ }^{a} \mu_{w}}\)when ^{w}μ_{g} is the R.I. of glass w.r.t. water.

→ ^{a}μ_{b} = \(\frac{1}{{ }^{b} \mu_{a}}\)

→ Refraction formula when the refraction takes place at convex spherical surface from rarer to denser medium for real image of object is:

– \(\frac{\mu_{1}}{u}+\frac{\mu_{2}}{v}=\frac{\mu_{2}-\mu_{1}}{R}\)

→ For virtual image, it is again same.

→ When refraction takes place from denser to rarer medium; it is given by

– \(\frac{\mu_{2}}{u}+\frac{\mu_{1}}{v}=\frac{\mu_{1}-\mu_{2}}{R}\)

→ Lens formula is

– \(\frac{1}{\mathrm{u}}+\frac{1}{\mathrm{v}}=\frac{1}{\mathrm{f}}\)

→ Lens Maker’s formula is

\(\frac{1}{f}\) = (μ – 1)(\frac{1}{R_{1}}-\frac{1}{R_{2}})

→ Power of a lens is given by

P = \(\frac{1}{\mathrm{f}(\mathrm{m})}\) (Dioptre) or D

→ Linear magnification produced by a lens:

m = \(\frac{1}{\mathrm{O}}=\frac{v}{\mathrm{u}}=\frac{\mathrm{f}}{\mathrm{f}+\mathrm{u}}=\frac{\mathrm{f}-v}{\mathrm{f}}\)

→ Focal length of combination of two lenses placed in contact is

\(\frac{1}{\mathrm{~F}}=\frac{1}{\mathrm{f}_{1}}+\frac{1}{\mathrm{f}_{2}}\)

→ Power of combination is

P = P_{1} + P_{2}

→ When the two lenses are placed at a distance ‘d’; then

\(\frac{1}{\mathrm{~F}}=\frac{1}{\mathrm{f}_{1}}+\frac{1}{\mathrm{f}_{2}}-\frac{\mathrm{d}}{\mathrm{f}_{1} \mathrm{f}_{2}}\)

→ Power of spherical refracting surface is

P = \(\frac{\mu_{2}-\mu_{1}}{R}\)

→ Lateral shift is given by

d = \(\frac{t}{\cos r}\) sin (i – r)

→ Magnification produced by lens combination is

m = m_{1} × m_{2}

→ For a prism,

- A = r
_{1}+ r_{2} - μ = \(\frac{\sin \left(\mathrm{A}+\delta_{\mathrm{m}}\right) / 2}{\sin \frac{\mathrm{A}}{2}}\)
- A + δ = i + e.
- For small angled prism, δ = (μ – 1)A.

→ Dispersive power is

W = δ_{v} – δ_{r} /δ = \(\frac{\mu_{v}-\mu_{r}}{\mu-1}\)

→ Condition for no deviation:

\(\frac{\mathrm{A}^{\prime}}{\mathrm{A}}=-\frac{(\mu-1)}{(\mu-1)}\)

net angular dispersion = δ (ω – ω’)

→ Condition for no dispersion:

1. \(\frac{\mathrm{A}^{\prime}}{\mathrm{A}}=-\frac{\mu_{\mathrm{v}}-\mu_{\mathrm{r}}}{\mu_{\mathrm{v}}-\mu_{\mathrm{r}}}\)

2. \(\frac{\omega}{\omega^{\prime}}=-\frac{\delta^{\prime}}{\delta}\)

Net deviation = δ(1 – \(\frac{\omega}{\omega^{\prime}}\))

→ Chromatic aberration is

f_{r} – f_{v} = w × f

→ Magnifying power of simple microscope is given by:

m = \(\frac{\beta}{\alpha}\) = 1 + \(\frac{\mathrm{D}}{\mathrm{f}}\)

When image is formed at infinity, then M = \(\frac{\mathrm{D}}{\mathrm{f}}\)

→ For compound microscope

M = \(\frac{v_{0}}{u_{0}}\)(1 + \(\frac{D}{f_{e}}\)) = – \(\frac{\mathrm{L}}{\mathrm{f}_{0}}\)(1 + \(\frac{D}{f_{e}}\))

→ Magnifying power of astronomical telescope for

1. nor mal adjustment is:

M = – \(\frac{\mathrm{f}_{0}}{\mathrm{f}_{\mathrm{e}}}\)

2. When final image is formed at least distance of distinct vision:

M = – \(\frac{\mathrm{f}_{0}}{\mathrm{f}_{\mathrm{e}}}\)(1 + \(\frac{\mathrm{f}_{\mathrm{e}}}{\mathrm{D}}\))

where f_{0}, f_{e} are the focal lengths of objective and eye piece respectively.

D = least distance of distinct vision.

→ Length of: (a) astronomical telescope tube for normal adjustment is given by

L = f_{0} + f_{e}

(b) Terrestrial telescope is

L = f_{o} + 4f + f_{e}e

where f is the focal length of the erecting lens.

→ For a mirror, f = \(\frac{\mathrm{R}}{2}\) , where f, R are the focal length and radius of

curvature of the spherical mirror.

→ Mirror formula is \(\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\)

→ Linear magnification produced by a mirror is

m = \(\frac{\mathrm{I}}{\mathrm{O}}=-\frac{\mathrm{v}}{\mathrm{u}}=\frac{\mathrm{f}}{\mathrm{f}-\mathrm{u}}=\frac{\mathrm{f}-\mathrm{v}}{\mathrm{f}}\)

→ Resolving power of telescope is given by

R.P = \(\frac{\mathrm{d}}{1.22 \lambda}\)

→ Angular limit of resolution of a telescope is

dθ = \(\frac{1}{\text { R.P. }}=\frac{1.22 \lambda}{d}\)

→ Brightness of telescope ∝ πr² ∝ \(\frac{\pi \mathrm{d}^{2}}{4}\)

where d = diameter of the objective lens.

→ Areal magnification = \(\frac{\text { Area of image }}{\text { Area of object }}=\frac{\mathrm{I}^{2}}{\mathrm{O}^{2}}\) = m^{2}