Given:
\(\mathrm{f}=-15 \mathrm{~cm}, \mathrm{u}=-10 \mathrm{~cm}, \mathrm{v}=?, \mathrm{~h}=3 \mathrm{~cm} \)
\(\frac{1}{f} =\frac{1}{v}-\frac{1}{u}  \Rightarrow \frac{1}{v}-\frac{1}{u} =\frac{1}{f} \)
\(\frac{1}{v} =\frac{1}{f}+\frac{1}{u}  \)

\(\frac{1}{v}=\frac{-5}{30}=-\frac{1}{6} \)
\(v=-6 \mathrm{~cm} \)
Size of the image:
Magnification \(=\frac{+v}{u} \quad\left(m=\frac{h^{\prime}}{h}\right)  \)
\(\frac{h^{\prime}}{h} =\frac{-v}{u}  \)
\(\frac{h^{\prime}}{3} =\frac{-6}{-10}=0.6  \)
\(h^{\prime} =0.6 \times 3=1.8 \mathrm{~cm}\)
Size of the image =1.8 cm

Given:
\(\mathrm{f}=10 \mathrm{~cm}, \mathrm{u}=-20 \mathrm{~cm}, \mathrm{v}=?  \)
\(\frac{1}{f}=\frac{1}{v}-\frac{1}{u}  \Rightarrow \frac{1}{v} =\frac{1}{f}+\frac{1}{u} \)
\(\frac{1}{v} =\frac{1}{10}+\frac{1}{-20}=\frac{1}{10}-\frac{1}{20}  \)
\(\frac{1}{v} =\frac{2-1}{20}=\frac{1}{20}  \)
\(\mathbf{v} =20 \mathrm{~cm}  \)
Image distance = 20 cm
Nature of image:
Nature of the image is real, enlarged and inverted image.

The eyes of the nocturnal birds like owl have a large cornea and a large pupil. These features increase their field of vision and also shows an increase in retinal surface and help them to collect more ambient light during night.

a) Yes, he got the image. But the image is not clear.
b) There is no change in the focal length. Because, no change in radius of curvature.

Compound microscope:
A Compound microscope is used to see the tiny objects has better magnification power than simple microscope.
Construction:
(i) A compound microscope consists of two convex lenses.
(ii) The lens with the shorter focal length is placed near the object, and is called as 'objective lens' or 'objective piece'.
(iii) The lens with larger focal length and larger aperture placed near the observer's eye is called as 'eye lens' or 'eye piece'.
(iv) Both the lenses are fixed in a narrow tube with adjustable provision.
Working:
(i) The object (AB) is placed at a distance slightly greater than the focal length of objective lens \(\left(u>f_{0}\right)\).
(ii) A real, inverted and magnified image \(\left(\mathrm{A}^{\prime} \mathrm{B}^{\prime}\right)\) is formed at the other side of the objective lens.
(iii) This image behaves as the object for the eye lens.
(iv) The position of the eye lens is adjusted in such a way, that the image (A' B') falls within the principal focus of the eye piece.
(v) This eye piece forms a virtual, enlarged and erect image (A" B") on the same side of the object.
(vi) Compound microscope has 50 to 200 times more magnification power than simple microscope.

Rules for obtaining images:
(i) When an object is placed in front of a lens, the light rays from the object fall on the lens.
(ii) The position, size and nature of the image formed can be understood only if we know certain basic rules.
Rule-1: When a ray of light strikes the convex lens obliquely at its optical centre, it continues to follow its path without any deviation.

Rule-2: When rays parallel to the principal axis strikes a convex or concave lens, the rays are refracted converged to (convex lens) or appear to diverge from the principal focus.

Rule-3: When a ray passing through (convex lens) or directed towards (concave lens) the principal focus strikes a convex or concave lens, the refracted ray will be parallel to the principal axis.

(i) Light is a form of energy.
(ii) Light always travels along a straight line.
(iii) Light does not need any medium for its propagation. It can even travel through vacuum.
(iv) The speed of light in vacuum or air is, c = 3 x 10⁸ m/s
(v) Since, light is in the form of waves, it is characterized by a wavelength (λ) and a frequency (v), which are related by the following equation: c = v λ (c - velocity of light).