An object viewed from a near point distance of 25 cm, using a microscopic lens with magnification '6', gives an unresolved image. A resolved image is observed at infinite distance with a total magnification double the earlier using an eyepiece along with the given lens and a tube of length 0.6 m, if the focal length of the eyepiece is equal to __________ cm.

A galaxy is moving away from the earth at a speed of 286 kms^$$-$$1. The shift in the wavelength of a redline at 630 nm is x $$\times$$ 10^$$-$$10 m. The value of x, to the nearest integer, is ____________. [Take the value of speed of light c, as 3 $$\times$$ 10⁸ ms^$$-$$1]

The image of an object placed in air formed by a convex refracting surface is at a distance of 10 m behind the surface. The image is real and is at $${{{2^{rd}}} \over 3}$$ of the distance of the object from the surface. The wavelength of light inside the surface is $${2 \over 3}$$ times the wavelength in air. The radius of the curved surface is $${x \over {13}}$$ m. The value of 'x' is ___________.

A deviation of 2$$^\circ$$ is produced in the yellow ray when prism of crown and flint glass are achromatically combined. Taking dispersive powers of crown and flint glass as 0.02 and 0.03 respectively and refractive index for yellow light for these glasses are 1.5 and 1.6 respectively. The refracting angles for crown glass prism will be ____________$$^\circ$$ (in degree). (Round off to the Nearest Integer)