1
JEE Main 2018 (Online) 15th April Morning Slot
+4
-1
A planoconvex lens becomes an optical system of $$28$$ $$cm$$ focal length when its plane surface is silvered and illuminated from left to right as shown in Fig-A.

If the same lens is instead silvered on the curved surface and illuminated from other side as in Fig-B, it acts like an optical system of focal length $$10$$ $$cm.$$ The refractive index of the material of lens is :

A
$$1.50$$
B
$$1.55$$
C
$$1.75$$
D
$$1.51$$
2
JEE Main 2018 (Online) 15th April Morning Slot
+4
-1
A particle is oscillating on the $$X$$-axis with an amplitude $$2$$ $$cm$$ about the point $${x_0} = 10\,cm,$$ with a frequency $$\omega$$. A concave mirror of local length $$5$$ $$cm$$ is placed at the origin (see figure).

Identify the correct statements.
A
The image executs periodic motoin.
B
The image executes non-periodic motion.
C
The turning points of the image are asymmetric w.r.t. the image of the point at $$x=10$$ $$cm$$.
D
The distance between the turning points of the oscillation of the image is $${{100} \over {21}}\,cm.$$
3
JEE Main 2017 (Online) 9th April Morning Slot
+4
-1
In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 20 cm from the lens. The focal length of the convex mirror is :
A
27.5 cm
B
20.0 cm
C
25.0 cm
D
30.5 cm
4
JEE Main 2017 (Online) 8th April Morning Slot
+4
-1
Let the refractive index of a denser medium with respect to a rarer medium be n12 and its critical angle be θC . At an angle of incidence A when light is travelling from denser medium to rarer medium, a part of the light is reflected and the rest is refracted and the angle between reflected and refracted rays is 90o. Angle A is given by :
A
$${1 \over {{{\cos }^{ - 1}}\left( {\sin {\theta _C}} \right)}}$$
B
$${1 \over {{{\tan }^{ - 1}}\left( {\sin {\theta _C}} \right)}}$$
C
$${\cos ^{ - 1}}\,\left( {\sin {\theta _C}} \right)$$
D
$${\tan ^{ - 1}}\,\left( {\sin {\theta _C}} \right)$$
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